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  Subjects -> MATHEMATICS (Total: 874 journals)
    - APPLIED MATHEMATICS (71 journals)
    - GEOMETRY AND TOPOLOGY (19 journals)
    - MATHEMATICS (647 journals)
    - MATHEMATICS (GENERAL) (41 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (77 journals)

MATHEMATICS (647 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: 7)
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: 11)
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: 10)
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: 3)
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: 18)
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: 21)
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: 2)
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: 14)
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: 12)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
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: 5)
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 Archive for Mathematical Logic
  [SJR: 0.946]   [H-I: 23]   [1 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1432-0665 - ISSN (Online) 0933-5846
   Published by Springer-Verlag Homepage  [2345 journals]
  • The subcompleteness of Magidor forcing
    • Authors: Gunter Fuchs
      Abstract: It is shown that the Magidor forcing to collapse the cofinality of a measurable cardinal that carries a length \(\omega _1\) sequence of normal ultrafilters, increasing in the Mitchell order, to \(\omega _1\) , is subcomplete.
      PubDate: 2017-06-20
      DOI: 10.1007/s00153-017-0568-1
       
  • A null ideal for inaccessibles
    • Authors: Sy-David Friedman; Giorgio Laguzzi
      Abstract: In this paper we introduce a tree-like forcing notion extending some properties of the random forcing in the context of \(2^\kappa \) , \(\kappa \) inaccessible, and study its associated ideal of null sets and notion of measurability. This issue was addressed by Shelah (On CON(Dominating \(\_\) lambda \(\,>\,\) cov \(\_\lambda \) (meagre)), arXiv:0904.0817, Problem 0.5) and concerns the definition of a forcing which is \(\kappa ^\kappa \) -bounding, \(<\kappa \) -closed and \(\kappa ^+\) -cc, for \(\kappa \) inaccessible. Cohen and Shelah (Generalizing random real forcing for inaccessible cardinals, arXiv:1603.08362) provide a proof for (Shelah, On CON(Dominating \(\_\) lambda \(\,>\,\) cov \(\_\lambda \) (meagre)), arXiv:0904.0817, Problem 0.5), and in this paper we independently reprove this result by using a different type of construction. This also contributes to a line of research adressed in the survey paper (Khomskii et al. in Math L Q 62(4–5):439–456, 2016).
      PubDate: 2017-06-19
      DOI: 10.1007/s00153-017-0562-7
       
  • l -Groups C ( X ) in continuous logic
    • Authors: Philip Scowcroft
      Abstract: In the context of continuous logic, this paper axiomatizes both the class \(\mathcal {C}\) of lattice-ordered groups isomorphic to C(X) for X compact and the subclass \(\mathcal {C}^+\) of structures existentially closed in \(\mathcal {C}\) ; shows that the theory of \(\mathcal {C}^+\) is \(\aleph _0\) -categorical and admits elimination of quantifiers; establishes a Nullstellensatz for \(\mathcal {C}\) and \(\mathcal {C}^+\) ; shows that \(C(X)\in \mathcal {C}\) has a prime-model extension in \(\mathcal {C}^+\) just in case X is Boolean; and proves that in a sense relevant to continuous logic, positive formulas admit in \(\mathcal {C}^+\) elimination of quantifiers to positive formulas.
      PubDate: 2017-06-15
      DOI: 10.1007/s00153-017-0566-3
       
  • Interpretable groups in Mann pairs
    • Authors: Haydar Göral
      Abstract: In this paper, we study an algebraically closed field \(\Omega \) expanded by two unary predicates denoting an algebraically closed proper subfield k and a multiplicative subgroup \(\Gamma \) . This will be a proper expansion of algebraically closed field with a group satisfying the Mann property, and also pairs of algebraically closed fields. We first characterize the independence in the triple \((\Omega , k, \Gamma )\) . This enables us to characterize the interpretable groups when \(\Gamma \) is divisible. Every interpretable group H in \((\Omega ,k, \Gamma )\) is, up to isogeny, an extension of a direct sum of k-rational points of an algebraic group defined over k and an interpretable abelian group in \(\Gamma \) by an interpretable group N, which is the quotient of an algebraic group by a subgroup \(N_1\) , which in turn is isogenous to a cartesian product of k-rational points of an algebraic group defined over k and an interpretable abelian group in \(\Gamma \) .
      PubDate: 2017-06-07
      DOI: 10.1007/s00153-017-0565-4
       
  • Baumgartner’s isomorphism problem for $$\aleph _2$$ ℵ 2 -dense
           suborders of $$\mathbb {R}$$ R
    • Authors: Justin Tatch Moore; Stevo Todorcevic
      Abstract: In this paper we will analyze Baumgartner’s problem asking whether it is consistent that \(2^{\aleph _0} \ge \aleph _2\) and every pair of \(\aleph _2\) -dense subsets of \(\mathbb {R}\) are isomorphic as linear orders. The main result is the isolation of a combinatorial principle \((**)\) which is immune to c.c.c. forcing and which in the presence of \(2^{\aleph _0} \le \aleph _2\) implies that two \(\aleph _2\) -dense sets of reals can be forced to be isomorphic via a c.c.c. poset. Also, it will be shown that it is relatively consistent with ZFC that there exists an \(\aleph _2\) dense suborder X of \(\mathbb {R}\) which cannot be embedded into \(-X\) in any outer model with the same \(\aleph _2\) .
      PubDate: 2017-06-06
      DOI: 10.1007/s00153-017-0549-4
       
  • Creature forcing and five cardinal characteristics in Cichoń’s
           diagram
    • Authors: Arthur Fischer; Martin Goldstern; Jakob Kellner; Saharon Shelah
      Abstract: We use a (countable support) creature construction to show that consistently $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}(\mathcal N)< {{\mathrm{non}}}(\mathcal M)< {{\mathrm{non}}}(\mathcal N)< {{\mathrm{cof}}}(\mathcal N) < 2^{\aleph _0}. \end{aligned}$$ The same method shows the consistency of $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}(\mathcal N)< {{\mathrm{non}}}(\mathcal N)< {{\mathrm{non}}}(\mathcal M)< {{\mathrm{cof}}}(\mathcal N) < 2^{\aleph _0}. \end{aligned}$$
      PubDate: 2017-06-03
      DOI: 10.1007/s00153-017-0553-8
       
  • Ordinal notation systems corresponding to Friedman’s linearized
           well-partial-orders with gap-condition
    • Authors: Michael Rathjen; Jeroen Van der Meeren; Andreas Weiermann
      Abstract: In this article we investigate whether the following conjecture is true or not: does the addition-free theta functions form a canonical notation system for the linear versions of Friedman’s well-partial-orders with the so-called gap-condition over a finite set of n labels. Rather surprisingly, we can show this is the case for two labels, but not for more than two labels. To this end, we determine the order type of the notation systems for addition-free theta functions in terms of ordinals less than \(\varepsilon _0\) . We further show that the maximal order type of the Friedman ordering can be obtained by a certain ordinal notation system which is based on specific binary theta functions.
      PubDate: 2017-06-02
      DOI: 10.1007/s00153-017-0559-2
       
  • Some remarks on Baire’s grand theorem
    • Authors: Riccardo Camerlo; Jacques Duparc
      Abstract: We provide a game theoretical proof of the fact that if f is a function from a zero-dimensional Polish space to \( \mathbb N^{\mathbb N}\) that has a point of continuity when restricted to any non-empty compact subset, then f is of Baire class 1. We use this property of the restrictions to compact sets to give a generalisation of Baire’s grand theorem for functions of any Baire class.
      PubDate: 2017-06-01
      DOI: 10.1007/s00153-017-0563-6
       
  • Codings and strongly inaccessible cardinals
    • Authors: Tadatoshi Miyamoto
      Abstract: We show that a coding principle introduced by J. Moore with respect to all ladder systems is equiconsistent with the existence of a strongly inaccessible cardinal. We also show that a coding principle introduced by S. Todorcevic has consistency strength at least of a strongly inaccessible cardinal.
      PubDate: 2017-05-29
      DOI: 10.1007/s00153-017-0548-5
       
  • Two applications of finite side conditions at $$\omega _2$$ ω 2
    • Authors: Itay Neeman
      Abstract: We present two applications of forcing with finite sequences of models as side conditions, adding objects of size \(\omega _2\) . The first involves adding a \(\Box _{\omega _1}\) sequence and variants of such sequences. The second involves adding partial weak specializing functions for trees of height \(\omega _2\) .
      PubDate: 2017-05-27
      DOI: 10.1007/s00153-017-0550-y
       
  • Saturation and solvability in abstract elementary classes with
           amalgamation
    • Authors: Sebastien Vasey
      Abstract: Theorem 0.1 Let \(\mathbf {K}\) be an abstract elementary class (AEC) with amalgamation and no maximal models. Let \(\lambda > {LS}(\mathbf {K})\) . If \(\mathbf {K}\) is categorical in \(\lambda \) , then the model of cardinality \(\lambda \) is Galois-saturated. This answers a question asked independently by Baldwin and Shelah. We deduce several corollaries: \(\mathbf {K}\) has a unique limit model in each cardinal below \(\lambda \) , (when \(\lambda \) is big-enough) \(\mathbf {K}\) is weakly tame below \(\lambda \) , and the thresholds of several existing categoricity transfers can be improved. We also prove a downward transfer of solvability (a version of superstability introduced by Shelah): Corollary 0.2 Let \(\mathbf {K}\) be an AEC with amalgamation and no maximal models. Let \(\lambda> \mu > {LS}(\mathbf {K})\) . If \(\mathbf {K}\) is solvable in \(\lambda \) , then \(\mathbf {K}\) is solvable in \(\mu \) .
      PubDate: 2017-05-27
      DOI: 10.1007/s00153-017-0561-8
       
  • Uniform proofs of ACC representations
    • Authors: Sam Buss
      Abstract: We give a uniform proof of the theorems of Yao and Beigel–Tarui representing ACC predicates as constant depth circuits with \(\hbox {MOD}_{m}\) gates and a symmetric gate. The proof is based on a relativized, generalized form of Toda’s theorem expressed in terms of closure properties of formulas under bounded universal, existential and modular counting quantifiers. This allows the main proofs to be expressed in terms of formula classes instead of Boolean circuits. The uniform version of the Beigel–Tarui theorem is then obtained automatically via the Furst–Saxe–Sipser and Paris–Wilkie translations. As a special case, we obtain a uniform version of Razborov and Smolensky’s representation of \(\hbox {AC}^{0}[p]\) circuits. The paper is partly expository, but is also motivated by the desire to recast Toda’s theorem, the Beigel–Tarui theorem, and their proofs into the language of bounded arithmetic. However, no knowledge of bounded arithmetic is needed.
      PubDate: 2017-05-26
      DOI: 10.1007/s00153-017-0560-9
       
  • Interpretability suprema in Peano Arithmetic
    • Authors: Paula Henk; Albert Visser
      Abstract: This paper develops the philosophy and technology needed for adding a supremum operator to the interpretability logic \(\mathsf {ILM}\) of Peano Arithmetic ( \(\mathsf {PA}\) ). It is well-known that any theories extending \(\mathsf {PA}\) have a supremum in the interpretability ordering. While provable in \(\mathsf {PA}\) , this fact is not reflected in the theorems of the modal system \(\mathsf {ILM}\) , due to limited expressive power. Our goal is to enrich the language of \(\mathsf {ILM}\) by adding to it a new modality for the interpretability supremum. We explore different options for specifying the exact meaning of the new modality. Our final proposal involves a unary operator, the dual of which can be seen as a (nonstandard) provability predicate satisfying the axioms of the provability logic \(\mathsf {GL}\) .
      PubDate: 2017-05-26
      DOI: 10.1007/s00153-017-0557-4
       
  • The sharp for the Chang model is small
    • Authors: William J. Mitchell
      Abstract: Woodin has shown that if there is a measurable Woodin cardinal then there is, in an appropriate sense, a sharp for the Chang model. We produce, in a weaker sense, a sharp for the Chang model using only the existence of a cardinal \(\kappa \) having an extender of length \(\kappa ^{+\omega _1}\) .
      PubDate: 2017-05-25
      DOI: 10.1007/s00153-017-0547-6
       
  • A predicate extension of real valued logic
    • Authors: Stefano Baratella
      Abstract: We study a predicate extension of an unbounded real valued propositional logic that has been recently introduced. The latter, in turn, can be regarded as an extension of both the abelian logic and of the propositional continuous logic. Among other results, we prove that our predicate extension satisfies the property of weak completeness (the equivalence between satisfiability and consistency) and, under an additional assumption on the set of premisses, the property of strong completeness (the equivalence between logical consequence and provability). Eventually we discuss some topological properties of the space of types in our logic.
      PubDate: 2017-05-25
      DOI: 10.1007/s00153-017-0558-3
       
  • The nonstationary ideal on $$P_\kappa (\lambda )$$ P κ ( λ ) for
           $$\lambda $$ λ singular
    • Authors: Pierre Matet; Saharon Shelah
      Abstract: We give a new characterization of the nonstationary ideal on \(P_\kappa (\lambda )\) in the case when \(\kappa \) is a regular uncountable cardinal and \(\lambda \) a singular strong limit cardinal of cofinality at least \(\kappa \) .
      PubDate: 2017-05-19
      DOI: 10.1007/s00153-017-0552-9
       
  • A herbrandized functional interpretation of classical first-order logic
    • Authors: Fernando Ferreira; Gilda Ferreira
      Abstract: We introduce a new typed combinatory calculus with a type constructor that, to each type \(\sigma \) , associates the star type \(\sigma ^*\) of the nonempty finite subsets of elements of type \(\sigma \) . We prove that this calculus enjoys the properties of strong normalization and confluence. With the aid of this star combinatory calculus, we define a functional interpretation of first-order predicate logic and prove a corresponding soundness theorem. It is seen that each theorem of classical first-order logic is connected with certain formulas which are tautological in character. As a corollary, we reprove Herbrand’s theorem on the extraction of terms from classically provable existential statements.
      PubDate: 2017-05-19
      DOI: 10.1007/s00153-017-0555-6
       
  • In memoriam: James Earl Baumgartner (1943–2011)
    • Authors: J. A. Larson
      Abstract: James Earl Baumgartner (March 23, 1943–December 28, 2011) came of age mathematically during the emergence of forcing as a fundamental technique of set theory, and his seminal research changed the way set theory is done. He made fundamental contributions to the development of forcing, to our understanding of uncountable orders, to the partition calculus, and to large cardinals and their ideals. He promulgated the use of logic such as absoluteness and elementary submodels to solve problems in set theory, he applied his knowledge of set theory to a variety of areas in collaboration with other mathematicians, and he encouraged a community of mathematicians with engaging survey talks, enthusiastic discussions of open problems, and friendly mathematical conversations.
      PubDate: 2017-05-18
      DOI: 10.1007/s00153-017-0546-7
       
  • Minimal elementary end extensions
    • Authors: James H. Schmerl
      Abstract: Suppose that \({\mathcal M}\models \mathsf{PA}\) and \({\mathfrak X} \subseteq {\mathcal P}(M)\) . If \({\mathcal M}\) has a finitely generated elementary end extension \({\mathcal N}\succ _\mathsf{end} {\mathcal M}\) such that \(\{X \cap M : X \in {{\mathrm{Def}}}({\mathcal N})\} = {\mathfrak X}\) , then there is such an \({\mathcal N}\) that is, in addition, a minimal extension of \({\mathcal M}\) iff every subset of M that is \(\Pi _1^0\) -definable in \(({\mathcal M}, {\mathfrak X})\) is the countable union of \(\Sigma _1^0\) -definable sets.
      PubDate: 2017-05-15
      DOI: 10.1007/s00153-017-0556-5
       
  • On constructions with 2-cardinals
    • Authors: Piotr Koszmider
      Abstract: We propose developing the theory of consequences of morasses relevant in mathematical applications in the language alternative to the usual one, replacing commonly used structures by families of sets originating with Velleman’s neat simplified morasses called 2-cardinals. The theory of related trees, gaps, colorings of pairs and forcing notions is reformulated and sketched from a unifying point of view with the focus on the applicability to constructions of mathematical structures like Boolean algebras, Banach spaces or compact spaces. The paper is dedicated to the memory of Jim Baumgartner whose seminal joint paper (Baumgartner and Shelah in Ann Pure Appl Logic 33(2):109–129, 1987) with Saharon Shelah provided a critical mass in the theory in question. A new result which we obtain as a side product is the consistency of the existence of a function \(f:[\lambda ^{++}]^2\rightarrow [\lambda ^{++}]^{\le \lambda }\) with the appropriate \(\lambda ^+\) -version of property \(\Delta \) for regular \(\lambda \ge \omega \) satisfying \(\lambda ^{<\lambda }=\lambda \) .
      PubDate: 2017-05-15
      DOI: 10.1007/s00153-017-0544-9
       
 
 
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