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  Subjects -> MATHEMATICS (Total: 867 journals)
    - APPLIED MATHEMATICS (69 journals)
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    - MATHEMATICS (645 journals)
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MATHEMATICS (645 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 10)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 5)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 9)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access  
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 17)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 7)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 17)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)

        1 2 3 4 | Last

Journal Cover Annals of Pure and Applied Logic
  [SJR: 1.19]   [H-I: 33]   [2 followers]  Follow
    
  This is an Open Access Journal Open Access journal
   ISSN (Print) 0168-0072
   Published by Elsevier Homepage  [3031 journals]
  • Proof lengths for instances of the Paris–Harrington principle

    • Authors: Anton Freund
      Pages: 1361 - 1382
      Abstract: Publication date: July 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 7
      Author(s): Anton Freund
      As Paris and Harrington have famously shown, Peano Arithmetic does not prove that for all numbers k , m , n there is an N which satisfies the statement PH ( k , m , n , N ) : For any k-coloring of its n-element subsets the set { 0 , … , N − 1 } has a large homogeneous subset of size ≥m. At the same time very weak theories can establish the Σ 1 -statement ∃ N PH ( k ‾ , m ‾ , n ‾ , N ) for any fixed parameters k , m , n . Which theory, then, does it take to formalize natural proofs of these instances? It is known that ∀ m ∃ N PH ( k ‾ , m , n ‾ , N ) has a natural and short proof (relative to n and k) by Σ n − 1 -induction. In contrast, we show that there is an elementary function e such that any proof of ∃ N PH ( e ( n ) ‾ , n + 1 ‾ , n ‾ , N ) by Σ n − 2 -induction is ridiculously long. In order to establish this result on proof lengths we give a computational analysis of slow provability, a notion introduced by Sy-David Friedman, Rathjen and Weiermann. We will see that slow uniform Σ 1 -reflection is related to a function that has a considerably lower growth rate than F ε 0 but dominates all functions F α with α < ε 0 in the fast-growing hierarchy.

      PubDate: 2017-05-01T14:19:49Z
      DOI: 10.1016/j.apal.2017.01.004
       
  • The Gamma question for many-one degrees

    • Authors: Matthew Harrison-Trainor
      Pages: 1396 - 1405
      Abstract: Publication date: July 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 7
      Author(s): Matthew Harrison-Trainor
      A set A is coarsely computable with density r ∈ [ 0 , 1 ] if there is an algorithm for deciding membership in A which always gives a (possibly incorrect) answer, and which gives a correct answer with density at least r. To any Turing degree a we can assign a value Γ T ( a ) : the minimum, over all sets A in a, of the highest density at which A is coarsely computable. The closer Γ T ( a ) is to 1, the closer a is to being computable. Andrews, Cai, Diamondstone, Jockusch, and Lempp noted that Γ T can take on the values 0, 1/2, and 1, but not any values in strictly between 1/2 and 1. They asked whether the value of Γ T can be strictly between 0 and 1/2. This is the Gamma question. Replacing Turing degrees by many-one degrees, we get an analogous question, and the same arguments show that Γ m can take on the values 0, 1/2, and 1, but not any values strictly between 1/2 and 1. We will show that for any r ∈ [ 0 , 1 / 2 ] , there is an m-degree a with Γ m ( a ) = r . Thus the range of Γ m is [ 0 , 1 / 2 ] ∪ { 1 } . Benoit Monin has recently announced a solution to the Gamma question for Turing degrees. Interestingly, his solution gives the opposite answer: the only possible values of Γ T are 0, 1/2, and 1.

      PubDate: 2017-05-01T14:19:49Z
      DOI: 10.1016/j.apal.2017.01.006
       
  • Propositional team logics

    • Authors: Fan Yang; Jouko Väänänen
      Pages: 1406 - 1441
      Abstract: Publication date: July 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 7
      Author(s): Fan Yang, Jouko Väänänen
      We consider team semantics for propositional logic, continuing [34]. In team semantics the truth of a propositional formula is considered in a set of valuations, called a team, rather than in an individual valuation. This offers the possibility to give meaning to concepts such as dependence, independence and inclusion. We associate with every formula ϕ based on finitely many propositional variables the set 〚 ϕ 〛 of teams that satisfy ϕ. We define a maximal propositional team logic in which every set of teams is definable as 〚 ϕ 〛 for suitable ϕ. This requires going beyond the logical operations of classical propositional logic. We exhibit a hierarchy of logics between the smallest, viz. classical propositional logic, and the maximal propositional team logic. We characterize these different logics in several ways: first syntactically by their logical operations, and then semantically by the kind of sets of teams they are capable of defining. In several important cases we are able to find complete axiomatizations for these logics.

      PubDate: 2017-05-01T14:19:49Z
      DOI: 10.1016/j.apal.2017.01.007
       
  • Neostability in countable homogeneous metric spaces

    • Authors: Gabriel Conant
      Pages: 1442 - 1471
      Abstract: Publication date: July 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 7
      Author(s): Gabriel Conant
      Given a countable, totally ordered commutative monoid R = ( R , ⊕ , ≤ , 0 ) , with least element 0, there is a countable, universal and ultrahomogeneous metric space U R with distances in R . We refer to this space as the R -Urysohn space, and consider the theory of U R in a binary relational language of distance inequalities. This setting encompasses many classical structures of varying model theoretic complexity, including the rational Urysohn space, the free nth roots of the complete graph (e.g. the random graph when n = 2 ), and theories of refining equivalence relations (viewed as ultrametric spaces). We characterize model theoretic properties of Th ( U R ) by algebraic properties of R , many of which are first-order in the language of ordered monoids. This includes stability, simplicity, and Shelah's SOP n -hierarchy. Using the submonoid of idempotents in R , we also characterize superstability, supersimplicity, and weak elimination of imaginaries. Finally, we give necessary conditions for elimination of hyperimaginaries, which further develops previous work of Casanovas and Wagner.

      PubDate: 2017-05-01T14:19:49Z
      DOI: 10.1016/j.apal.2017.01.008
       
  • The uniform content of partial and linear orders

    • Authors: Eric P. Astor; Damir D. Dzhafarov; Reed Solomon; Jacob Suggs
      Pages: 1153 - 1171
      Abstract: Publication date: June 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 6
      Author(s): Eric P. Astor, Damir D. Dzhafarov, Reed Solomon, Jacob Suggs
      The principle ADS asserts that every linear order on ω has an infinite ascending or descending sequence. This has been studied extensively in the reverse mathematics literature, beginning with the work of Hirschfeldt and Shore [16]. We introduce the principle ADC , which asserts that every such linear order has an infinite ascending or descending chain. The two are easily seen to be equivalent over the base system RCA 0 of second order arithmetic; they are even computably equivalent. However, we prove that ADC is strictly weaker than ADS under Weihrauch (uniform) reducibility. In fact, we show that even the principle SADS , which is the restriction of ADS to linear orders of type ω + ω ⁎ , is not Weihrauch reducible to ADC . In this connection, we define a more natural stable form of ADS that we call General - SADS , which is the restriction of ADS to linear orders of type k + ω , ω + ω ⁎ , or ω + k , where k is a finite number. We define General - SADC analogously. We prove that General - SADC is not Weihrauch reducible to SADS , and so in particular, each of SADS and SADC is strictly weaker under Weihrauch reducibility than its general version. Finally, we turn to the principle CAC , which asserts that every partial order on ω has an infinite chain or antichain. This has two previously studied stable variants, SCAC and WSCAC , which were introduced by Hirschfeldt and Jockusch [16], and by Jockusch, Kastermans, Lempp, Lerman, and Solomon [19], respectively, and which are known to be equivalent over RCA 0 . Here, we show that SCAC is strictly weaker than WSCAC under even computable reducibility.

      PubDate: 2017-04-02T17:28:22Z
      DOI: 10.1016/j.apal.2016.11.010
       
  • Dominating the Erdős–Moser theorem in reverse mathematics

    • Authors: Ludovic Patey
      Pages: 1172 - 1209
      Abstract: Publication date: June 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 6
      Author(s): Ludovic Patey
      The Erdős–Moser theorem ( EM ) states that every infinite tournament has an infinite transitive subtournament. This principle plays an important role in the understanding of the computational strength of Ramsey's theorem for pairs ( RT 2 2 ) by providing an alternate proof of RT 2 2 in terms of EM and the ascending descending sequence principle ( ADS ). In this paper, we study the computational weakness of EM and construct a standard model (ω-model) of simultaneously EM , weak König's lemma and the cohesiveness principle, which is not a model of the atomic model theorem. This separation answers a question of Hirschfeldt, Shore and Slaman, and shows that the weakness of the Erdős–Moser theorem goes beyond the separation of EM from ADS proven by Lerman, Solomon and Towsner.

      PubDate: 2017-04-02T17:28:22Z
      DOI: 10.1016/j.apal.2016.11.011
       
  • The countable admissible ordinal equivalence relation

    • Authors: William Chan
      Pages: 1224 - 1246
      Abstract: Publication date: June 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 6
      Author(s): William Chan
      Let F ω 1 be the countable admissible ordinal equivalence relation defined on 2 ω by x F ω 1 y if and only if ω 1 x = ω 1 y . Some invariant descriptive set theoretic properties of F ω 1 will be explored using infinitary logic in countable admissible fragments as the main tool. Marker showed F ω 1 is not the orbit equivalence relation of a continuous action of a Polish group on 2 ω . Becker stengthened this to show F ω 1 is not even the orbit equivalence relation of a Δ 1 1 action of a Polish group. However, Montalbán has shown that F ω 1 is Δ 1 1 reducible to an orbit equivalence relation of a Polish group action, in fact, F ω 1 is classifiable by countable structures. It will be shown here that F ω 1 must be classified by structures of high Scott rank. Let E ω 1 denote the equivalence of order types of reals coding well-orderings. If E and F are two equivalence relations on Polish spaces X and Y, respectively, E ≤ a Δ 1 1 F denotes the existence of a Δ 1 1 function f : X → Y which is a reduction of E to F, except possibly on countably many classes of E. Using a result of Zapletal, the existence of a measurable cardinal implies E ω 1 ≤ a Δ 1 1 F ω 1 . However, it will be shown that in Gödel's constructible universe L (and set generic extensions of L), E ω 1 ≤ a Δ 1 1 F ω 1 is false. Lastly, the techniques of the previous result will be used to show that in L (and set gener...
      PubDate: 2017-04-02T17:28:22Z
      DOI: 10.1016/j.apal.2016.12.002
       
  • Bar recursion over finite partial functions

    • Authors: Paulo Oliva; Thomas Powell
      Pages: 887 - 921
      Abstract: Publication date: May 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 5
      Author(s): Paulo Oliva, Thomas Powell
      We introduce a new, demand-driven variant of Spector's bar recursion in the spirit of the Berardi–Bezem–Coquand functional of [4]. The recursion takes place over finite partial functions u, where the control parameter ω, used in Spector's bar recursion to terminate the computation at sequences s satisfying ω ( s ˆ ) < s , now acts as a guide for deciding exactly where to make bar recursive updates, terminating the computation whenever ω ( u ˆ ) ∈ dom ( u ) . We begin by exploring theoretical aspects of this new form of recursion, then in the main part of the paper we show that demand-driven bar recursion can be directly used to give an alternative functional interpretation of classical countable choice. We provide a short case study as an illustration, in which we extract a new bar recursive program from the proof that there is no injection from N → N to N , and compare this with the program that would be obtained using Spector's original variant. We conclude by formally establishing that our new bar recursor is primitive recursively equivalent to the original Spector bar recursion, and thus defines the same class of functionals when added to Gödel's system T .

      PubDate: 2017-03-08T09:28:37Z
      DOI: 10.1016/j.apal.2016.11.003
       
  • Mitchell's theorem revisited

    • Authors: Thomas Gilton; John Krueger
      Pages: 922 - 1016
      Abstract: Publication date: May 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 5
      Author(s): Thomas Gilton, John Krueger
      Mitchell's theorem on the approachability ideal states that it is consistent relative to a greatly Mahlo cardinal that there is no stationary subset of ω 2 ∩ cof ( ω 1 ) in the approachability ideal I [ ω 2 ] . In this paper we give a new proof of Mitchell's theorem, deriving it from an abstract framework of side condition methods.

      PubDate: 2017-03-08T09:28:37Z
      DOI: 10.1016/j.apal.2016.11.004
       
  • Honest elementary degrees and degrees of relative provability without the
           cupping property

    • Authors: Paul Shafer
      Pages: 1017 - 1031
      Abstract: Publication date: May 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 5
      Author(s): Paul Shafer
      An element a of a lattice cups to an element b > a if there is a c < b such that a ∪ c = b . An element of a lattice has the cupping property if it cups to every element above it. We prove that there are non-zero honest elementary degrees that do not have the cupping property, which answers a question of Kristiansen, Schlage-Puchta, and Weiermann. In fact, we show that if b is a sufficiently large honest elementary degree, then b has the anti-cupping property, which means that there is an a with 0 < E a < E b that does not cup to b. For comparison, we also modify a result of Cai to show, in several versions of the degrees of relative provability that are closely related to the honest elementary degrees, that in fact all non-zero degrees have the anti-cupping property, not just sufficiently large degrees.

      PubDate: 2017-03-08T09:28:37Z
      DOI: 10.1016/j.apal.2016.11.005
       
  • Spatial logic of tangled closure operators and modal mu-calculus

    • Authors: Robert Goldblatt; Ian Hodkinson
      Pages: 1032 - 1090
      Abstract: Publication date: May 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 5
      Author(s): Robert Goldblatt, Ian Hodkinson
      There has been renewed interest in recent years in McKinsey and Tarski's interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the modal mu-calculus and to a logic of tangled closure operators that was developed by Fernández-Duque after these two languages had been shown by Dawar and Otto to have the same expressive power over finite transitive Kripke models. We prove that this equivalence remains true over topological spaces. We extend the McKinsey–Tarski topological ‘dissection lemma’. We also take advantage of the fact (proved by us elsewhere) that various tangled closure logics with and without the universal modality ∀ have the finite model property in Kripke semantics. These results are used to construct a representation map (also called a d-p-morphism) from any dense-in-itself metric space X onto any finite connected locally connected serial transitive Kripke frame. This yields completeness theorems over X for a number of languages: (i) the modal mu-calculus with the closure operator ◇; (ii) ◇ and the tangled closure operators 〈 t 〉 (in fact 〈 t 〉 can express ◇); (iii) ◇ , ∀ ; (iv) ◇ , ∀ , 〈 t 〉 ; (v) the derivative operator 〈 d 〉 ; (vi) 〈 d 〉 and the associated tangled closure operators 〈 d t 〉 ; (vii) 〈 d 〉 , ∀ ; (viii) 〈 d 〉 , ∀ , 〈 d t 〉 . Soundness also holds, if: (a) for languages with ∀, X is connected; (b) for languages with 〈 d 〉 , X validates the well-known axiom G 1 . For countable languages without ∀, we prove strong completeness. We also show that in the presence of ∀, strong completeness fails if X is compact and locally connected.

      PubDate: 2017-03-08T09:28:37Z
      DOI: 10.1016/j.apal.2016.11.006
       
  • Characterizing model-theoretic dividing lines via collapse of generalized
           indiscernibles

    • Authors: Vincent Guingona; Cameron Donnay Hill; Lynn Scow
      Pages: 1091 - 1111
      Abstract: Publication date: May 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 5
      Author(s): Vincent Guingona, Cameron Donnay Hill, Lynn Scow
      We use the notion of collapse of generalized indiscernible sequences to classify various model theoretic dividing lines. In particular, we use collapse of n-multi-order indiscernibles to characterize op-dimension n; collapse of function-space indiscernibles (i.e. parameterized equivalence relations) to characterize rosy theories; and finally, convex equivalence relation indiscernibles to characterize NTP2 theories.

      PubDate: 2017-03-08T09:28:37Z
      DOI: 10.1016/j.apal.2016.11.007
       
  • Characterizing large cardinals in terms of layered posets

    • Authors: Sean Cox; Philipp Lücke
      Pages: 1112 - 1131
      Abstract: Publication date: May 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 5
      Author(s): Sean Cox, Philipp Lücke
      Given an uncountable regular cardinal κ, a partial order is κ-stationarily layered if the collection of regular suborders of P of cardinality less than κ is stationary in P κ ( P ) . We show that weak compactness can be characterized by this property of partial orders by proving that an uncountable regular cardinal κ is weakly compact if and only if every partial order satisfying the κ-chain condition is κ-stationarily layered. We prove a similar result for strongly inaccessible cardinals. Moreover, we show that the statement that all κ-Knaster partial orders are κ-stationarily layered implies that κ is a Mahlo cardinal and every stationary subset of κ reflects. This shows that this statement characterizes weak compactness in canonical inner models. In contrast, we show that it is also consistent that this statement holds at a non-weakly compact cardinal.

      PubDate: 2017-03-08T09:28:37Z
      DOI: 10.1016/j.apal.2016.11.008
       
  • Germinal theories in Łukasiewicz logic

    • Authors: Leonardo Manuel Cabrer; Daniele Mundici
      Pages: 1132 - 1151
      Abstract: Publication date: May 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 5
      Author(s): Leonardo Manuel Cabrer, Daniele Mundici
      Differently from boolean logic, in Łukasiewicz infinite-valued propositional logic Ł∞ the theory Θ max ⁡ , v consisting of all formulas satisfied by a model v ∈ [ 0 , 1 ] n is not the only one having v as its unique model: indeed, there is a smallest such theory Θ min ⁡ , v , the germinal theory at v, which in general is strictly contained in Θ max ⁡ , v . The Lindenbaum algebra of Θ max ⁡ , v is promptly seen to coincide with the subalgebra of the standard MV-algebra [ 0 , 1 ] generated by the coordinates of v. The description of the Lindenbaum algebras of germinal theories in two variables is our main aim in this paper. As a basic prerequisite of independent interest, we prove that for any models v and w the germinal theories Θ min ⁡ , v and Θ min ⁡ , w have isomorphic Lindenbaum algebras iff v and w have the same orbit under the action of the affine group over the integers.

      PubDate: 2017-03-08T09:28:37Z
      DOI: 10.1016/j.apal.2016.11.009
       
  • Polish G-spaces and continuous logic

    • Authors: A. Ivanov; B. Majcher-Iwanow
      Pages: 749 - 775
      Abstract: Publication date: April 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 4
      Author(s): A. Ivanov, B. Majcher-Iwanow
      We extend the generalised model theory of H. Becker from [2] to the case of Polish G-spaces when G is an arbitrary Polish group. Our approach is inspired by logic actions of Polish groups which arise in continuous logic.

      PubDate: 2017-02-04T06:18:23Z
      DOI: 10.1016/j.apal.2016.11.002
       
  • Covering the recursive sets

    • Authors: Bjørn Kjos-Hanssen; Frank Stephan; Sebastiaan A. Terwijn
      Pages: 804 - 823
      Abstract: Publication date: April 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 4
      Author(s): Bjørn Kjos-Hanssen, Frank Stephan, Sebastiaan A. Terwijn
      We give solutions to two of the questions in a paper by Brendle, Brooke-Taylor, Ng and Nies. Our examples derive from a 2014 construction by Khan and Miller as well as new direct constructions using martingales. At the same time, we introduce the concept of i.o. subuniformity and relate this concept to recursive measure theory. We prove that there are classes closed downwards under Turing reducibility that have recursive measure zero and that are not i.o. subuniform. This shows that there are examples of classes that cannot be covered with methods other than probabilistic ones. It is easily seen that every set of hyperimmune degree can cover the recursive sets. We prove that there are both examples of hyperimmune-free degree that can and that cannot compute such a cover.

      PubDate: 2017-02-04T06:18:23Z
      DOI: 10.1016/j.apal.2016.10.017
       
  • Ordinals and graph decompositions

    • Authors: Stephen Flood
      Pages: 824 - 839
      Abstract: Publication date: April 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 4
      Author(s): Stephen Flood
      The theory of simplicial graph decompositions studies the infinite graphs that are built from a sequence of irreducible graphs which are attached together at complete subgraphs. In this paper, we study the logical complexity of deciding if a graph is prime decomposable. A large part of this analysis involves determining which ordinals must appear in these types of decompositions. A result of Diestel says that every countable simplicial tree decomposition can be rearranged to have length at most ω. We show that no such ordinal bound can be found for the lengths of non-tree decompositions. More generally, we show that for each ordinal σ, there is a decomposable graph whose shortest simplicial decomposition has length exactly σ. Adapting this argument, we show that the index set of decomposable computable graphs DECOMP is Π 1 1 hard by showing that WO is 1-reducible to DECOMP .

      PubDate: 2017-02-04T06:18:23Z
      DOI: 10.1016/j.apal.2016.10.016
       
  • Computable neighbourhoods of points in semicomputable manifolds

    • Authors: Zvonko Iljazović; Lucija Validžić
      Pages: 840 - 859
      Abstract: Publication date: April 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 4
      Author(s): Zvonko Iljazović, Lucija Validžić
      We examine conditions under which a semicomputable set in a computable metric space contains computable points. We prove that computable points in a semicomputable set S are dense if S is a manifold (possibly with boundary) or S has the topological type of a polyhedron. Moreover, we find conditions under which a point in some set has a computable compact neighbourhood in that set. In particular, we show that a point x in a semicomputable set has a computable compact neighbourhood if x has a neighbourhood homeomorphic to Euclidean space.

      PubDate: 2017-02-04T06:18:23Z
      DOI: 10.1016/j.apal.2016.10.015
       
  • Randomness for computable measures and initial segment complexity

    • Authors: Rupert Hölzl; Christopher P. Porter
      Pages: 860 - 886
      Abstract: Publication date: April 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 4
      Author(s): Rupert Hölzl, Christopher P. Porter
      We study the possible growth rates of the Kolmogorov complexity of initial segments of sequences that are random with respect to some computable measure on 2 ω , the so-called proper sequences. Our main results are as follows: (1) We show that the initial segment complexity of a proper sequence X is bounded from below by a computable function (that is, X is complex) if and only if X is random with respect to some computable, continuous measure. (2) We prove that a uniform version of the previous result fails to hold: there is a family of complex sequences that are random with respect to a single computable measure such that for every computable, continuous measure μ, some sequence in this family fails to be random with respect to μ. (3) We show that there are proper sequences with extremely slow-growing initial segment complexity, that is, there is a proper sequence the initial segment complexity of which is infinitely often below every computable function, and even a proper sequence the initial segment complexity of which is dominated by all computable functions. (4) We prove various facts about the Turing degrees of such sequences and show that they are useful in the study of certain classes of pathological measures on 2 ω , namely diminutive measures and trivial measures.

      PubDate: 2017-02-04T06:18:23Z
      DOI: 10.1016/j.apal.2016.10.014
       
  • Representation and duality of the untyped λ-calculus in nominal lattice
           and topological semantics, with a proof of topological completeness

    • Authors: Murdoch J. Gabbay; Michael Gabbay
      Pages: 501 - 621
      Abstract: Publication date: March 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 3
      Author(s): Murdoch J. Gabbay, Michael Gabbay
      We give a semantics for the λ-calculus based on a topological duality theorem in nominal sets. A novel interpretation of λ is given in terms of adjoints, and λ-terms are interpreted absolutely as sets (no valuation is necessary).

      PubDate: 2017-02-04T06:18:23Z
      DOI: 10.1016/j.apal.2016.10.001
       
  • Distance structures for generalized metric spaces

    • Authors: Gabriel Conant
      Pages: 622 - 650
      Abstract: Publication date: March 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 3
      Author(s): Gabriel Conant
      Let R = ( R , ⊕ , ≤ , 0 ) be an algebraic structure, where ⊕ is a commutative binary operation with identity 0, and ≤ is a translation-invariant total order with least element 0. Given a distinguished subset S ⊆ R , we define the natural notion of a “generalized” R -metric space, with distances in S. We study such metric spaces as first-order structures in a relational language consisting of a distance inequality for each element of S. We first construct an ordered additive structure S ⁎ on the space of quantifier-free 2-types consistent with the axioms of R -metric spaces with distances in S, and show that, if A is an R -metric space with distances in S, then any model of Th ( A ) logically inherits a canonical S ⁎ -metric. Our primary application of this framework concerns countable, universal, and homogeneous metric spaces, obtained as generalizations of the rational Urysohn space. We adapt previous work of Delhommé, Laflamme, Pouzet, and Sauer to fully characterize the existence of such spaces. We then fix a countable totally ordered commutative monoid R , with least element 0, and consider U R , the countable Urysohn space over R . We show that quantifier elimination for Th ( U R ) is characterized by continuity of addition in R ⁎ , which can be expressed as a first-order sentence of R in the language of ordered monoids. Finally, we analyze an example of Casanovas and Wagner in this context.

      PubDate: 2017-02-04T06:18:23Z
      DOI: 10.1016/j.apal.2016.10.002
       
  • Downward categoricity from a successor inside a good frame

    • Authors: Sebastien Vasey
      Pages: 651 - 692
      Abstract: Publication date: March 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 3
      Author(s): Sebastien Vasey
      In the setting of abstract elementary classes (AECs) with amalgamation, Shelah has proven a downward categoricity transfer from categoricity in a successor and Grossberg and VanDieren have established an upward transfer assuming in addition a locality property for Galois types that they called tameness. We further investigate categoricity transfers in tame AECs. We use orthogonality calculus to prove a downward transfer from categoricity in a successor in AECs that have a good frame (a forking-like notion for types of singletons) on an interval of cardinals: Theorem 0.1 Let K be an AEC and let LS ( K ) ≤ λ < θ be cardinals. If K has a type-full good [ λ , θ ] -frame and K is categorical in both λ and θ + , then K is categorical in all μ ∈ [ λ , θ ] . We deduce improvements on the threshold of several categoricity transfers that do not mention frames. For example, the threshold in Shelah's transfer can be improved from ℶ ℶ ( 2 LS ( K ) ) + to ℶ ( 2 LS ( K ) ) + assuming that the AEC is LS ( K ) -tame. The successor hypothesis can also be removed from Shelah's result by assuming in addition either that the AEC has primes over sets of the form M ∪ { a } or (using an unpublished claim of Shelah) that the weak generalized continuum hypothesis holds.

      PubDate: 2017-02-04T06:18:23Z
      DOI: 10.1016/j.apal.2016.10.003
       
  • Full-splitting Miller trees and infinitely often equal reals

    • Abstract: Publication date: August 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 8
      Author(s): Yurii Khomskii, Giorgio Laguzzi
      We investigate two closely related partial orders of trees on ω ω : the full-splitting Miller trees and the infinitely often equal trees, as well as their corresponding σ-ideals. The former notion was considered by Newelski and Rosłanowski while the latter involves a correction of a result of Spinas. We consider some Marczewski-style regularity properties based on these trees, which turn out to be closely related to the property of Baire, and look at the dichotomies of Newelski–Rosłanowski and Spinas for higher projective pointclasses. We also provide some insight concerning a question of Fremlin whether one can add an infinitely often equal real without adding a Cohen real, which was recently solved by Zapletal.

      PubDate: 2017-05-21T15:55:03Z
       
  • On the decidability of the theory of modules over the ring of algebraic
           integers

    • Abstract: Publication date: August 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 8
      Author(s): Sonia L'Innocente, Carlo Toffalori, Gena Puninski
      We will prove that the theory of all modules over the ring of algebraic integers is decidable.

      PubDate: 2017-05-21T15:55:03Z
       
  • Universal graphs at ℵω1+1

    • Authors: Jacob Davis
      Abstract: Publication date: Available online 3 May 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Jacob Davis
      Starting from a supercompact cardinal we build a model in which 2 ℵ ω 1 = 2 ℵ ω 1 + 1 = ℵ ω 1 + 3 but there is a jointly universal family of size ℵ ω 1 + 2 of graphs on ℵ ω 1 + 1 . The same technique will work for any uncountable cardinal in place of ω 1 .

      PubDate: 2017-05-07T14:48:17Z
      DOI: 10.1016/j.apal.2017.04.005
       
  • Reducts of the Henson graphs with a constant

    • Abstract: Publication date: July 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 7
      Author(s): András Pongrácz
      Let ( H n , E ) denote the Henson graph, the unique countable homogeneous graph whose age consists of all finite K n -free graphs. In this note the reducts of the Henson graphs with a constant are determined up to first-order interdefinability. It is shown that up to first-order interdefinability ( H 3 , E , 0 ) has 13 reducts and ( H n , E , 0 ) has 16 reducts for n ≥ 4 .

      PubDate: 2017-05-01T14:19:49Z
       
  • Addendum to: “The Bolzano–Weierstrass theorem is the jump of weak
           Kőnig's lemma” [Ann. Pure Appl. Logic 163 (6) (2012) 623–655]

    • Authors: Vasco Brattka; Andrea Cettolo; Guido Gherardi; Alberto Marcone; Matthias Schröder
      Abstract: Publication date: Available online 29 April 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Vasco Brattka, Andrea Cettolo, Guido Gherardi, Alberto Marcone, Matthias Schröder
      The purpose of this addendum is to close a gap in the proof of [1, Theorem 11.2], which characterizes the computational content of the Bolzano–Weierstraß Theorem for arbitrary computable metric spaces.

      PubDate: 2017-05-01T14:19:49Z
      DOI: 10.1016/j.apal.2017.04.004
       
  • Imaginaries in bounded pseudo real closed fields

    • Authors: Samaria Montenegro
      Abstract: Publication date: Available online 21 April 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Samaria Montenegro
      The main result of this paper is that if M is a bounded PRC field, then T h ( M ) eliminates imaginaries in the language of rings expanded by constant symbols. As corollary of the elimination of imaginaries and the fact that the algebraic closure (in the sense of model theory) defines a pregeometry we obtain that the complete theory of a bounded PRC field is superrosy of U th -rank 1.

      PubDate: 2017-04-23T21:52:32Z
      DOI: 10.1016/j.apal.2017.04.003
       
  • Finding a field in a Zariski-like structure

    • Authors: Kaisa Kangas
      Abstract: Publication date: Available online 6 April 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Kaisa Kangas
      We show that if M is a Zariski-like structure (see [6]) and the canonical pregeometry obtained from the bounded closure operator (bcl) is non locally modular, then M interprets either an algebraically closed field or a non-classical group.

      PubDate: 2017-04-09T20:53:23Z
      DOI: 10.1016/j.apal.2017.04.002
       
  • Ceres in Intuitionistic Logic

    • Authors: David Cerna; Alexander Leitsch; Giselle Reis; Simon Wolfsteiner
      Abstract: Publication date: Available online 5 April 2017
      Source:Annals of Pure and Applied Logic
      Author(s): David Cerna, Alexander Leitsch, Giselle Reis, Simon Wolfsteiner
      In this paper we present a procedure allowing the extension of a CERES-based cut-elimination method to intuitionistic logic. Previous results concerning this problem manage to capture fragments of intuitionistic logic, but in many essential cases structural constraints were violated during normal form construction resulting in a classical proof. The heart of the CERES method is the resolution calculus, which ignores the structural constraints of the well known intuitionistic sequent calculi. We propose, as a method of avoiding the structural violations, the generalization of resolution from the resolving of clauses to the resolving of cut-free proofs, in other words, what we call proof resolution. The result of proof resolution is a cut-free proof rather than a clause. Note that resolution on ground clauses is essentially atomic cut, thus using proof resolution to construct cut-free proofs one would need to join the two proofs together and remove the atoms which where resolved. To efficiently perform this joining (and guarantee that the resulting cut-free proof is intuitionistic) we develop the concept of proof subsumption (similar to clause subsumption) and indexed resolution, a refinement indexing atoms by their corresponding positions in the cut formula. Proof subsumption serves as a tool to prove the completeness of the new method CERES-i, and indexed resolution provides an efficient strategy for the joining of two proofs which is in general a nondeterministic search. Such a refinement is essential for any attempt to implement this method. Finally we compare the complexity of CERES-i with that of Gentzen-based methods.

      PubDate: 2017-04-09T20:53:23Z
      DOI: 10.1016/j.apal.2017.04.001
       
  • Condensational equivalence, equimorphism, elementary equivalence and
           similar similarities

    • Authors: Nenad
      Abstract: Publication date: June 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 6
      Author(s): Miloš S. Kurilić, Nenad Morača
      We investigate the interplay between several similarities of relational structures: the condensational equivalence (defined by X ∼ c Y iff there are bijective homomorphisms f : X → Y and g : Y → X ), the isomorphism, the equimorphism (bi-embedability), the elementary equivalence and the similarities of structures determined by some similarities of their self-embedding monoids. It turns out that the Hasse diagram describing the hierarchy of these equivalence relations restricted to the set Mod L ( κ ) of all L-structures of size κ collapses significantly for a finite cardinal κ or for a unary language L, while for infinite structures of non-unary languages we have a large diversity.

      PubDate: 2017-04-02T17:28:22Z
       
  • Abelian C-minimal valued groups

    • Authors: F. Delon; P. Simonetta
      Abstract: Publication date: Available online 29 March 2017
      Source:Annals of Pure and Applied Logic
      Author(s): F. Delon, P. Simonetta
      We classify abelian C-minimal valued groups up to pure and elementary extensions and small modifications. We define first the notion of almost regularity for abelian valued groups. Then we introduce on the chain of valuations the structure which enables us to characterize C-minimal abelian valued groups as the almost regular ones with an o-minimal chain.

      PubDate: 2017-04-02T17:28:22Z
      DOI: 10.1016/j.apal.2017.03.008
       
  • Superstability from categoricity in abstract elementary classes

    • Authors: Will Boney; Rami Grossberg; Monica M. VanDieren; Sebastien Vasey
      Abstract: Publication date: Available online 27 March 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Will Boney, Rami Grossberg, Monica M. VanDieren, Sebastien Vasey
      Starting from an abstract elementary class with no maximal models, Shelah and Villaveces have shown (assuming instances of diamond) that categoricity implies a superstability-like property for nonsplitting, a particular notion of independence. We generalize their result as follows: given any abstract notion of independence for Galois (orbital) types over models, we derive that the notion satisfies a superstability property provided that the class is categorical and satisfies a weakening of amalgamation. This extends the Shelah–Villaveces result (the independence notion there was splitting) as well as a result of the first and second author where the independence notion was coheir. The argument is in ZFC and fills a gap in the Shelah–Villaveces proof.

      PubDate: 2017-04-02T17:28:22Z
      DOI: 10.1016/j.apal.2017.01.005
       
  • Shelah's eventual categoricity conjecture in universal classes: Part I

    • Authors: Sebastien Vasey
      Abstract: Publication date: Available online 22 March 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Sebastien Vasey
      We prove: Theorem 0.1 Let K be a universal class. If K is categorical in cardinals of arbitrarily high cofinality, then K is categorical on a tail of cardinals. The proof stems from ideas of Adi Jarden and Will Boney, and also relies on a deep result of Shelah. As opposed to previous works, the argument is in ZFC and does not use the assumption of categoricity in a successor cardinal. The argument generalizes to abstract elementary classes (AECs) that satisfy a locality property and where certain prime models exist. Moreover assuming amalgamation we can give an explicit bound on the Hanf number and get rid of the cofinality restrictions: Theorem 0.2 Let K be an AEC with amalgamation. Assume that K is fully LS ( K ) -tame and short and has primes over sets of the form M ∪ { a } . Write H 2 : = ℶ ( 2 ℶ ( 2 LS ( K ) ) + ) + . If K is categorical in a λ > H 2 , then K is categorical in all λ ′ ≥ H 2 .

      PubDate: 2017-04-02T17:28:22Z
      DOI: 10.1016/j.apal.2017.03.003
       
  • Erratum to: “Scott rank of Polish metric spaces” [Ann. Pure Appl.
           Logic 165 (12) (2014) 1919–1929]

    • Authors: Michal Doucha
      Abstract: Publication date: Available online 21 March 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Michal Doucha


      PubDate: 2017-04-02T17:28:22Z
      DOI: 10.1016/j.apal.2017.03.006
       
  • Homology groups of types in stable theories and the Hurewicz
           correspondence

    • Authors: John Goodrick; Byunghan Kim; Alexei Kolesnikov
      Abstract: Publication date: Available online 18 March 2017
      Source:Annals of Pure and Applied Logic
      Author(s): John Goodrick, Byunghan Kim, Alexei Kolesnikov
      We give an explicit description of the homology group H n ( p ) of a strong type p in any stable theory under the assumption that for every non-forking extension q of p the groups H i ( q ) are trivial for 2 ≤ i < n . The group H n ( p ) turns out to be isomorphic to the automorphism group of a certain part of the algebraic closure of n independent realizations of p; it follows from the authors' earlier work that such a group must be abelian. We call this the “Hurewicz correspondence” by analogy with the Hurewicz Theorem in algebraic topology.

      PubDate: 2017-04-02T17:28:22Z
      DOI: 10.1016/j.apal.2017.03.007
       
  • The strength of infinitary Ramseyan principles can be accessed by their
           densities

    • Authors: Andrey Bovykin; Andreas Weiermann
      Abstract: Publication date: Available online 14 March 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Andrey Bovykin, Andreas Weiermann
      In this article, we conduct a model-theoretic investigation of three infinitary Ramseyan statements: the Infinite Ramsey Theorem for pairs and two colours ( RT 2 2 ), the Canonical Ramsey Theorem for pairs ( CRT 2 ) and the Regressive Ramsey Theorem for pairs ( RegRT 2 ). We approximate the logical strength of these principles by the strength of their first-order iterated versions, known as density principles. We then investigate their logical strength using strong initial segments of models of Peano Arithmetic, in the spirit of the classical article by Paris and Kirby, hereby re-proving old results model-theoretically. The article is concluded by a discussion of two further outreaches of densities. One is a further investigation of the strength of the Ramsey Theorem for pairs. The other deals with the asymptotics of the standard Ramsey function R 2 2 .

      PubDate: 2017-04-02T17:28:22Z
      DOI: 10.1016/j.apal.2017.03.005
       
  • Nullifying randomness and genericity using symmetric difference

    • Authors: Rutger Kuyper; Joseph S. Miller
      Abstract: Publication date: Available online 10 March 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Rutger Kuyper, Joseph S. Miller
      For a class C of sets, let us say that a set A is C stabilising if A △ X ∈ C for every X ∈ C . We prove that the Martin-Löf stabilising sets are exactly the K-trivial sets, as are the weakly 2-random stabilising sets. We also show that the 1-generic stabilising sets are exactly the computable sets.

      PubDate: 2017-03-12T16:37:07Z
      DOI: 10.1016/j.apal.2017.03.004
       
  • On generalized Van Benthem-type characterizations

    • Authors: Grigory K. Olkhovikov
      Abstract: Publication date: Available online 9 March 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Grigory K. Olkhovikov
      The paper continues the line of [6], [7], and [8]. This results in a model-theoretic characterization of expressive powers of arbitrary finite sets of guarded connectives of degree not exceeding 1 and regular connectives of degree 2 over the language of bounded lattices.

      PubDate: 2017-03-12T16:37:07Z
      DOI: 10.1016/j.apal.2017.03.002
       
  • Elementary recursive quantifier elimination based on Thom encoding and
           sign determination

    • Authors: Daniel Perrucci; Marie-Françoise Roy
      Abstract: Publication date: Available online 8 March 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Daniel Perrucci, Marie-Françoise Roy
      We describe a new quantifier elimination algorithm for real closed fields based on Thom encoding and sign determination. The complexity of this algorithm is elementary recursive and its proof of correctness is completely algebraic. In particular, the notion of connected components of semialgebraic sets is not used.

      PubDate: 2017-03-12T16:37:07Z
      DOI: 10.1016/j.apal.2017.03.001
       
  • Forking in short and tame abstract elementary classes

    • Authors: Will Boney; Rami Grossberg
      Abstract: Publication date: Available online 2 March 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Will Boney, Rami Grossberg
      We develop a notion of forking for Galois-types in the context of Elementary Classes (AECs). Under the hypotheses that an AEC K is tame, type-short, and failure of an order-property, we consider Definition 1 Let M 0 ≺ N be models from K and A be a set. We say that the Galois-type of A over N does not fork over M 0 , written A ⫝ M 0 N , iff for all small a ∈ A and all small N − ≺ N , we have that Galois-type of a over N − is realized in M 0 . Assuming property (E) (Existence and Extension, see Definition 3.3) we show that this non-forking is a well behaved notion of independence, in particular satisfies symmetry and uniqueness and has a corresponding U-rank. We find conditions for a universal local character, in particular derive superstability-like property from little more than categoricity in a “big cardinal”. Finally, we show that under large cardinal axioms the proofs are simpler and the non-forking is more powerful. In [10], it is established that, if this notion is an independence notion, then it is the only one.

      PubDate: 2017-03-08T09:28:37Z
      DOI: 10.1016/j.apal.2017.02.002
       
  • Disjoint Borel functions

    • Authors: Dan Hathaway
      Abstract: Publication date: Available online 1 March 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Dan Hathaway
      For each a ∈ ω ω , we define a Baire class one function f a : ω ω → ω ω which encodes a in a certain sense. We show that for each Borel g : ω ω → ω ω , f a ∩ g = ∅ implies a ∈ Δ 1 1 ( c ) where c is any code for g. We generalize this theorem for g in a larger pointclass Γ. Specifically, when Γ = Δ 2 1 , a ∈ L [ c ] . Also for all n ∈ ω , when Γ = Δ 3 + n 1 , a ∈ M 1 + n ( c ) .

      PubDate: 2017-03-02T08:54:36Z
      DOI: 10.1016/j.apal.2017.02.004
       
  • Supercompact extender based Magidor-Radin forcing

    • Authors: Carmi Merimovich
      Abstract: Publication date: Available online 28 February 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Carmi Merimovich
      The extender based Magidor-Radin forcing is being generalized to supercompact type extenders.

      PubDate: 2017-03-02T08:54:36Z
      DOI: 10.1016/j.apal.2017.02.006
       
  • CE-cell decomposition and open cell property in o-minimal structures

    • Authors: Somayyeh Tari
      Abstract: Publication date: Available online 28 February 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Somayyeh Tari
      Continuous extension cells, or CE-cells, are cells whose defining functions have continuous extensions on closure of their domains. An o-minimal structure has the CE-cell decomposition property if any cell decomposition has a refinement by CE-cells. If the o-minimal structure M has the CE-cell decomposition property, then it has the open cell property. In other words, every definable open set in M is a finite union of definable open cells. Here, we show that the open cell property does not imply the CE-cell decomposition property. Also, after introducing an existence of limit property, we show that the CE-cell decomposition property is equivalent to the open cell property and the existence of limit property.

      PubDate: 2017-03-02T08:54:36Z
      DOI: 10.1016/j.apal.2017.02.005
       
  • On non-self-referential fragments of modal logics

    • Authors: Junhua
      Abstract: Publication date: April 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 4
      Author(s): Junhua Yu
      Justification logics serve as “explicit” modal logics in a way that, formula ϕ is a modal theorem if and only if there is a justification theorem, called a realization of ϕ, gained by replacing modality occurrences in ϕ by (justification) terms with structures explicitly explaining their evidential contents. In justification logics, terms stand for justifications of (propositions expressed by) formulas, and as a kind of atomic terms, constants stand for that of (justification) axioms. Kuznets has shown that in order to realize (i.e., offer a realization of) some modal theorems, it is necessary to employ a self-referential constant, that is, a constant that stands for a justification of an axiom containing an occurrence of the constant itself. Based on existing works, including some of the author's, this paper treats the collection of modal theorems that are non-self-referentially realizable as a fragment (called non-self-referential fragment) of the modal logic, and verifies: (1) that fragment is not closed in general under modus ponens; and (2) that fragment is not “conservative” in general when going from a smaller modal logic to a larger one.

      PubDate: 2017-02-04T06:18:23Z
       
  • Polytopes and simplexes in p-adic fields

    • Authors: Luck
      Abstract: Publication date: Available online 6 January 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Luck Darnière
      We introduce topological notions of polytopes and simplexes, the latter being expected to fulfil in p-adically closed fields the function of real simplexes in the classical results of triangulation of semi-algebraic sets over real closed fields. We prove that the faces of every p-adic polytope are polytopes and that they form a rooted tree with respect to specialisation. Simplexes are then defined as polytopes whose faces tree is a chain. Our main result is a construction allowing to divide every p-adic polytope in a complex of p-adic simplexes with prescribed faces and shapes.

      PubDate: 2017-02-04T06:18:23Z
       
  • The ⁎-variation of the Banach–Mazur game and forcing axioms

    • Authors: Yasuo Yoshinobu
      Abstract: Publication date: Available online 6 January 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Yasuo Yoshinobu
      We introduce a property of posets which strengthens ( ω 1 + 1 ) -strategic closedness. This property is defined using a variation of the Banach–Mazur game on posets, where the first player chooses a countable set of conditions instead of a single condition at each turn. We prove PFA is preserved under any forcing over a poset with this property. As an application we reproduce a proof of Magidor's theorem about the consistency of PFA with some weak variations of the square principles. We also argue how different this property is from ( ω 1 + 1 ) -operational closedness, which we introduced in our previous work, by observing which portions of MA + ( ω 1 -closed ) are preserved or destroyed under forcing over posets with either property.

      PubDate: 2017-02-04T06:18:23Z
      DOI: 10.1016/j.apal.2017.01.003
       
  • On expansions of the real field by complex subgroups

    • Authors: Erin Caulfield
      Abstract: Publication date: Available online 6 January 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Erin Caulfield
      We construct a class of finite rank multiplicative subgroups of the complex numbers such that the expansion of the real field by such a group is model-theoretically well-behaved. As an application we show that a classification of expansions of the real field by cyclic multiplicative subgroups of the complex numbers due to Hieronymi does not even extend to expansions by subgroups with two generators.

      PubDate: 2017-02-04T06:18:23Z
      DOI: 10.1016/j.apal.2017.01.002
       
  • Unifying the model theory of first-order and second-order arithmetic via
           WKL0⁎

    • Authors: Ali Enayat; Tin Lok Wong
      Abstract: Publication date: Available online 2 January 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Ali Enayat, Tin Lok Wong
      We develop machinery to make the Arithmetized Completeness Theorem more effective in the study of many models of I Δ 0 + B Σ 1 + exp , including all countable ones, by passing on to the conservative extension WKL 0 ⁎ of I Δ 0 + B Σ 1 + exp . Our detailed study of the model theory of WKL 0 ⁎ leads to the simplification and improvement of many results in the model theory of Peano arithmetic and its fragments pertaining to the construction of various types of end extensions and initial segments.

      PubDate: 2017-02-04T06:18:23Z
      DOI: 10.1016/j.apal.2016.12.003
       
 
 
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