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MATHEMATICS (642 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
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: 3)
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 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: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 6)
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: 2)
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: 18)
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)
Foundations and Trends® in Networking     Full-text available via subscription   (Followers: 1)

        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  [2340 journals]
  • Coherent trees that are not Countryman
    • Authors: Yinhe Peng
      Pages: 237 - 251
      Abstract: Abstract First, we show that every coherent tree that contains a Countryman suborder is \({\mathbb {R}}\) -embeddable when restricted to a club. Then for a linear order O that can not be embedded into \(\omega \) , there exists (consistently) an \({{\mathbb {R}}}\) -embeddable O-ranging coherent tree which is not Countryman. And for a linear order \(O'\) that can not be embedded into \({\mathbb {Z}}\) , there exists (consistently) an \({\mathbb {R}}\) -embeddable \(O'\) -ranging coherent tree which contains no Countryman suborder. Finally, we will see that this is the best we can do.
      PubDate: 2017-05-01
      DOI: 10.1007/s00153-017-0530-2
      Issue No: Vol. 56, No. 3-4 (2017)
  • Some definable properties of sets in non-valuational weakly o-minimal
    • Authors: Somayyeh Tari
      Pages: 309 - 317
      Abstract: Abstract Let \({\mathcal {M}}=(M,<,+,\cdot ,\ldots )\) be a non-valuational weakly o-minimal expansion of a real closed field \((M,<,+,\cdot )\) . In this paper, we prove that \({\mathcal {M}}\) has a \(C^r\) -strong cell decomposition property, for each positive integer r, a best analogous result from Tanaka and Kawakami (Far East J Math Sci (FJMS) 25(3):417–431, 2007). We also show that curve selection property holds in non-valuational weakly o-minimal expansions of ordered groups. Finally, we extend the notion of definable compactness suitable for weakly o-minimal structures which was examined for definable sets (Peterzil and Steinhorn in J Lond Math Soc 295:769–786, 1999), and prove that a definable set is definably compact if and only if it is closed and bounded.
      PubDate: 2017-05-01
      DOI: 10.1007/s00153-017-0523-1
      Issue No: Vol. 56, No. 3-4 (2017)
  • An induction principle over real numbers
    • Authors: Assia Mahboubi
      Pages: 43 - 49
      Abstract: Abstract We give a constructive proof of the open induction principle on real numbers, using bar induction and enumerative open sets. We comment the algorithmic content of this result.
      PubDate: 2017-02-01
      DOI: 10.1007/s00153-016-0513-8
      Issue No: Vol. 56, No. 1-2 (2017)
  • Models of weak theories of truth
    • Authors: Mateusz Łełyk; Bartosz Wcisło
      Abstract: Abstract In the following paper we propose a model-theoretical way of comparing the “strength” of various truth theories which are conservative over \( PA \) . Let \({\mathfrak {Th}}\) denote the class of models of \( PA \) which admit an expansion to a model of theory \({ Th}\) . We show (combining some well known results and original ideas) that $$\begin{aligned} {{\mathfrak {PA}}}\supset {\mathfrak {TB}}\supset {{\mathfrak {RS}}}\supset {\mathfrak {UTB}}\supseteq \mathfrak {CT^-}, \end{aligned}$$ where \({\mathfrak {PA}}\) denotes simply the class of all models of \( PA \) and \({\mathfrak {RS}}\) denotes the class of recursively saturated models of \( PA \) . Our main original result is that every model of \( PA \) which admits an expansion to a model of \( CT ^-\) , admits also an expansion to a model of \( UTB \) . Moreover, as a corollary to one of the results (brought to us by Carlo Nicolai) we conclude that \( UTB \) is not relatively interpretable in \( TB \) , thus answering the question from Fujimoto (Bull Symb Log 16:305–344, 2010).
      PubDate: 2017-04-22
      DOI: 10.1007/s00153-017-0531-1
  • The reverse mathematics of non-decreasing subsequences
    • Authors: Ludovic Patey
      Abstract: Abstract Every function over the natural numbers has an infinite subdomain on which the function is non-decreasing. Motivated by a question of Dzhafarov and Schweber, we study the reverse mathematics of variants of this statement. It turns out that this statement restricted to computably bounded functions is computationally weak and does not imply the existence of the halting set. On the other hand, we prove that it is not a consequence of Ramsey’s theorem for pairs. This statement can therefore be seen as an arguably natural principle between the arithmetic comprehension axiom and stable Ramsey’s theorem for pairs.
      PubDate: 2017-04-21
      DOI: 10.1007/s00153-017-0536-9
  • A logic for arguing about probabilities in measure teams
    • Authors: Tapani Hyttinen; Gianluca Paolini; Jouko Väänänen
      Abstract: Abstract We use sets of assignments, a.k.a. teams, and measures on them to define probabilities of first-order formulas in given data. We then axiomatise first-order properties of such probabilities and prove a completeness theorem for our axiomatisation. We use the Hardy–Weinberg Principle of biology and the Bell’s Inequalities of quantum physics as examples.
      PubDate: 2017-04-13
      DOI: 10.1007/s00153-017-0535-x
  • The complexity of topological conjugacy of pointed Cantor minimal systems
    • Authors: Burak Kaya
      Abstract: Abstract In this paper, we analyze the complexity of topological conjugacy of pointed Cantor minimal systems from the point of view of descriptive set theory. We prove that the topological conjugacy relation on pointed Cantor minimal systems is Borel bireducible with the Borel equivalence relation \(\varDelta _{\mathbb {R}}^+\) on \(\mathbb {R}^{{\mathbb {N}}}\) defined by \(x \varDelta _{\mathbb {R}}^+y \Leftrightarrow \{x_i{:}\,i \in {\mathbb {N}}\}=\{y_i{:}\,i \in {\mathbb {N}}\}\) . Moreover, we show that \(\varDelta _{\mathbb {R}}^+\) is a lower bound for the Borel complexity of topological conjugacy of Cantor minimal systems. Finally, we interpret our results in terms of properly ordered Bratteli diagrams and discuss some applications.
      PubDate: 2017-04-03
      DOI: 10.1007/s00153-017-0534-y
  • Chains of saturated models in AECs
    • Authors: Will Boney; Sebastien Vasey
      Abstract: We study when a union of saturated models is saturated in the framework of tame abstract elementary classes (AECs) with amalgamation. We prove: Theorem 0.1. If K is a tame AEC with amalgamation satisfying a natural definition of superstability (which follows from categoricity in a high-enough cardinal), then for all high-enough \(\lambda {:}\) The union of an increasing chain of \(\lambda \) -saturated models is \(\lambda \) -saturated. There exists a type-full good \(\lambda \) -frame with underlying class the saturated models of size \(\lambda \) . There exists a unique limit model of size \(\lambda \) . Our proofs use independence calculus and a generalization of averages to this non first-order context.
      PubDate: 2017-04-03
      DOI: 10.1007/s00153-017-0532-0
  • Symmetry in abstract elementary classes with amalgamation
    • Authors: Monica M. VanDieren; Sebastien Vasey
      Abstract: This paper is part of a program initiated by Saharon Shelah to extend the model theory of first order logic to the non-elementary setting of abstract elementary classes (AECs). An abstract elementary class is a semantic generalization of the class of models of a complete first order theory with the elementary substructure relation. We examine the symmetry property of splitting (previously isolated by the first author) in AECs with amalgamation that satisfy a local definition of superstability. The key results are a downward transfer of symmetry and a deduction of symmetry from failure of the order property. These results are then used to prove several structural properties in categorical AECs, improving classical results of Shelah who focused on the special case of categoricity in a successor cardinal. We also study the interaction of symmetry with tameness, a locality property for Galois (orbital) types. We show that superstability and tameness together imply symmetry. This sharpens previous work of Boney and the second author.
      PubDate: 2017-03-28
      DOI: 10.1007/s00153-017-0533-z
  • A strong partition cardinal above $$\varTheta $$ Θ
    • Authors: Daniel W. Cunningham
      Abstract: Abstract Assuming \(\text {ZF}+\text {DC}\) , we prove that if there exists a strong partition cardinal greater than \(\varTheta \) , then (1) there is an inner model of \(\text {ZF}+\text {AD}+\text {DC}+ {{{\mathbb {R}}} }^{{\#}}\) exists, and (2) there is an inner model of \(\text {ZF}+\text {AD}+\text {DC}+ (\exists \kappa >\varTheta )\,(\kappa \) is measurable). Here \(\varTheta \) is the supremum of the ordinals which are the surjective image of the set of reals \({{{\mathbb {R}}} }\) .
      PubDate: 2017-03-18
      DOI: 10.1007/s00153-017-0529-8
  • The countable existentially closed pseudocomplemented semilattice
    • Authors: Joël Adler
      Abstract: Abstract As the class \(\mathcal {PCSL}\) of pseudocomplemented semilattices is a universal Horn class generated by a single finite structure it has a \(\aleph _0\) -categorical model companion \(\mathcal {PCSL}^*\) . As \(\mathcal {PCSL}\) is inductive the models of \(\mathcal {PCSL}^*\) are exactly the existentially closed models of \(\mathcal {PCSL}\) . We will construct the unique existentially closed countable model of \(\mathcal {PCSL}\) as a direct limit of algebraically closed pseudocomplemented semilattices.
      PubDate: 2017-03-17
      DOI: 10.1007/s00153-017-0527-x
  • An Easton like theorem in the presence of Shelah cardinals
    • Authors: Mohammad Golshani
      Abstract: Abstract We show that Shelah cardinals are preserved under the canonical \({{\mathrm{GCH}}}\) forcing notion. We also show that if \({{\mathrm{GCH}}}\) holds and \(F:{{\mathrm{REG}}}\rightarrow {{\mathrm{CARD}}}\) is an Easton function which satisfies some weak properties, then there exists a cofinality preserving generic extension of the universe which preserves Shelah cardinals and satisfies \(\forall \kappa \in {{\mathrm{REG}}},~ 2^{\kappa }=F(\kappa )\) . This gives a partial answer to a question asked by Cody (Arch Math Logic 52(5–6):569–591, 2013) and independently by Honzik (Acta Univ Carol 1:55–72, 2015). We also prove an indestructibility result for Shelah cardinals.
      PubDate: 2017-03-07
      DOI: 10.1007/s00153-017-0528-9
  • Reverse mathematics and order theoretic fixed point theorems
    • Authors: Takashi Sato; Takeshi Yamazaki
      Abstract: Abstract The theory of countable partially ordered sets (posets) is developed within a weak subsystem of second order arithmetic. We within \(\mathsf {RCA_0}\) give definitions of notions of the countable order theory and present some statements of countable lattices equivalent to arithmetical comprehension axiom over \(\mathsf {RCA_0}\) . Then we within \(\mathsf {RCA_0}\) give proofs of Knaster–Tarski fixed point theorem, Tarski–Kantorovitch fixed point theorem, Bourbaki–Witt fixed point theorem, and Abian–Brown maximal fixed point theorem for countable lattices or posets. We also give Reverse Mathematics results of the fixed point theory of countable posets; Abian–Brown least fixed point theorem, Davis’ converse for countable lattices, Markowski’s converse for countable posets, and arithmetical comprehension axiom are pairwise equivalent over \(\mathsf {RCA_0}\) . Here the converses state that some fixed point properties characterize the completeness of the underlying spaces.
      PubDate: 2017-02-27
      DOI: 10.1007/s00153-017-0526-y
  • A parallel to the null ideal for inaccessible $$\lambda $$ λ : Part I
    • Authors: Saharon Shelah
      Abstract: Abstract It is well known how to generalize the meagre ideal replacing \(\aleph _0\) by a (regular) cardinal \(\lambda > \aleph _0\) and requiring the ideal to be \(({<}\lambda )\) -complete. But can we generalize the null ideal? In terms of forcing, this means finding a forcing notion similar to the random real forcing, replacing \(\aleph _0\) by \(\lambda \) . So naturally, to call it a generalization we require it to be \(({<}\lambda )\) -complete and \(\lambda ^+\) -c.c. and more. Of course, we would welcome additional properties generalizing the ones of the random real forcing. Returning to the ideal (instead of forcing) we may look at the Boolean Algebra of \(\lambda \) -Borel sets modulo the ideal. Common wisdom have said that there is no such thing because we have no parallel of Lebesgue integral, but here surprisingly first we get a positive \(=\) existence answer for a generalization of the null ideal for a “mild” large cardinal \(\lambda \) —a weakly compact one. Second, we try to show that this together with the meagre ideal (for \(\lambda \) ) behaves as in the countable case. In particular, we consider the classical Cichoń diagram, which compares several cardinal characterizations of those ideals. We shall deal with other cardinals, and with more properties of related forcing notions in subsequent papers (Shelah in The null ideal for uncountable cardinals; Iterations adding no \(\lambda \) -Cohen; Random \(\lambda \) -reals for inaccessible continued; Creature iteration for inaccesibles. Preprint; Bounding forcing with chain conditions for uncountable cardinals) and Cohen and Shelah (On a parallel of random real forcing for inaccessible cardinals. arXiv:1603.08362 [math.LO]) and a joint work with Baumhauer and Goldstern.
      PubDate: 2017-02-20
      DOI: 10.1007/s00153-017-0524-0
  • The complexity of isomorphism for complete theories of linear orders with
           unary predicates
    • Authors: Richard Rast
      Abstract: Abstract Suppose A is a linear order, possibly with countably many unary predicates added. We classify the isomorphism relation for countable models of \(\text {Th}(A)\) up to Borel bi-reducibility, showing there are exactly five possibilities and characterizing exactly when each can occur in simple model-theoretic terms. We show that if the language is finite (in particular, if there are no unary predicates), then the theory is \(\aleph _0\) -categorical or Borel complete; this generalizes a theorem due to Schirmann (Theories des ordres totaux et relations dequivalence. Master’s thesis, Universite de Paris VII, 1997).
      PubDate: 2017-02-09
      DOI: 10.1007/s00153-017-0525-z
  • Magidor–Malitz reflection
    • Authors: Yair Hayut
      Abstract: Abstract In this paper we investigate the consistency and consequences of the downward Löwenheim–Skolem–Tarski theorem for extension of the first order logic by the Magidor–Malitz quantifier. We derive some combinatorial results and improve the known upper bound for the consistency of Chang’s conjecture at successor of singular cardinals.
      PubDate: 2017-02-06
      DOI: 10.1007/s00153-017-0522-2
  • A generalized Borel-reducibility counterpart of Shelah’s main gap
    • Authors: Tapani Hyttinen; Vadim Kulikov; Miguel Moreno
      Abstract: Abstract We study the \(\kappa \) -Borel-reducibility of isomorphism relations of complete first order theories in a countable language and show the consistency of the following: For all such theories T and \(T^{\prime }\) , if T is classifiable and \(T^{\prime }\) is not, then the isomorphism of models of \(T^{\prime }\) is strictly above the isomorphism of models of T with respect to \(\kappa \) -Borel-reducibility. In fact, we can also ensure that a range of equivalence relations modulo various non-stationary ideals are strictly between those isomorphism relations. The isomorphism relations are considered on models of some fixed uncountable cardinality obeying certain restrictions.
      PubDate: 2017-02-02
      DOI: 10.1007/s00153-017-0521-3
  • Relations between the $${\mathcal {I}}$$ I -ultrafilters
    • Authors: Jianyong Hong; Shuguo Zhang
      Abstract: Abstract Under CH we show the following results: There is a discrete ultrafilter which is not a \({\mathcal {Z}}_{0}\) -ultrafilter. There is a \(\sigma \) -compact ultrafilter which is not a \({\mathcal {Z}}_{0}\) -ultrafilter. There is a \({\mathcal {J}}_{\omega ^{3}}\) -ultrafilter which is not a \({\mathcal {Z}}_{0}\) -ultrafilter.
      PubDate: 2016-12-24
      DOI: 10.1007/s00153-016-0520-9
  • Definable types in the theory of closed ordered differential fields
    • Authors: Quentin Brouette
      Abstract: Abstract We study definable types in the theory of closed ordered differential fields (CODF). We show a condition for a type to be definable, then we prove that definable types are dense in the Stone space of CODF.
      PubDate: 2016-11-18
      DOI: 10.1007/s00153-016-0517-4
  • Constructions of categories of setoids from proof-irrelevant families
    • Abstract: Abstract When formalizing mathematics in constructive type theories, or more practically in proof assistants such as Coq or Agda, one is often using setoids (types with explicit equivalence relations). In this note we consider two categories of setoids with equality on objects and show, within intensional Martin-Löf type theory, that they are isomorphic. Both categories are constructed from a fixed proof-irrelevant family F of setoids. The objects of the categories form the index setoid I of the family, whereas the definition of arrows differs. The first category has for arrows triples \((a,b,f:F(a)\,\rightarrow \,F(b))\) where f is an extensional function. Two such arrows are identified if appropriate composition with transportation maps (given by F) makes them equal. In the second category the arrows are triples \((a,b,R \hookrightarrow \Sigma (I,F)^2)\) where R is a total functional relation between the subobjects \(F(a), F(b) \hookrightarrow \Sigma (I,F)\) of the setoid sum of the family. This category is simpler to use as the transportation maps disappear. Moreover we also show that the full image of a category along an E-functor into an E-category is a category.
      PubDate: 2016-11-01
      DOI: 10.1007/s00153-016-0514-7
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