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  Subjects -> MATHEMATICS (Total: 1041 journals)
    - APPLIED MATHEMATICS (84 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (770 journals)
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    - NUMERICAL ANALYSIS (23 journals)
    - PROBABILITIES AND MATH STATISTICS (98 journals)

MATHEMATICS (770 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 5)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
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: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 38)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
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: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 12)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 9)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 21)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 8)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 18)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 10)
Advances in Materials Science     Open Access   (Followers: 17)
Advances in Mathematical Physics     Open Access   (Followers: 7)
Advances in Mathematics     Full-text available via subscription   (Followers: 15)
Advances in Nonlinear Analysis     Open Access  
Advances in Numerical Analysis     Open Access   (Followers: 7)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 8)
Advances in Pure Mathematics     Open Access   (Followers: 9)
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: 7)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 13)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 2)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 11)
Anadol University Journal of Science and Technology B : Theoritical Sciences     Open Access  
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 6)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 3)
Annales Mathematicae Silesianae     Open Access   (Followers: 2)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – 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: 4)
Annals of Data Science     Hybrid Journal   (Followers: 13)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 7)
Annals of Mathematics     Full-text available via subscription   (Followers: 2)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
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  
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 1)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 14)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics     Open Access   (Followers: 8)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 10)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 4)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 6)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 4)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 25)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 3)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 5)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 2)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal   (Followers: 1)
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: 2)
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: 13)
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: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     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 Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chaos, Solitons & Fractals : X     Open Access  
ChemSusChem     Hybrid Journal   (Followers: 8)
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: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 15)
Commentarii Mathematici Helvetici     Hybrid Journal  
Communications in Advanced Mathematical Sciences     Open Access  
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 4)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 4)
Complex Analysis and its Synergies     Open Access   (Followers: 3)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus Mathematique     Full-text available via subscription  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
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: 10)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 8)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 15)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 31)
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: 4)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 2)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  

        1 2 3 4 | Last

Similar Journals
Journal Cover
Annals of Pure and Applied Logic
Journal Prestige (SJR): 1.38
Citation Impact (citeScore): 1
Number of Followers: 4  

  This is an Open Access Journal Open Access journal
ISSN (Print) 0168-0072
Published by Elsevier Homepage  [3181 journals]
  • Uniformly locally o-minimal structures and locally o-minimal structures
           admitting local definable cell decomposition

    • Abstract: Publication date: Available online 13 November 2019Source: Annals of Pure and Applied LogicAuthor(s): Masato Fujita We define and investigate a uniformly locally o-minimal structure of the second kind in this paper. All uniformly locally o-minimal structures of the second kind have local monotonicity, which is a local version of monotonicity theorem of o-minimal structures. We also demonstrate a local definable cell decomposition theorem for definably complete uniformly locally o-minimal structures of the second kind. We define dimension of a definable set and investigate its basic properties when the given structure is a locally o-minimal structure which admits local definable cell decomposition.
       
  • Functional representation of finitely generated free algebras in
           subvarieties of BL-algebras

    • Abstract: Publication date: Available online 11 November 2019Source: Annals of Pure and Applied LogicAuthor(s): Manuela Busaniche, José Luis Castiglioni, Noemí Lubomirsky Consider any subvariety of BL-algebras generated by a single BL-chain which is the ordinal sum of the standard MV-algebra on [0,1] and a basic hoop H. We present a geometrical characterization of elements in the finitely generated free algebra of each of these subvarieties. In this characterization there is a clear insight of the role of the regular and dense elements of the generating chain. As an application, we analyze maximal and prime filters in the free algebra.
       
  • Completeness theorems for σ–additive probabilistic
           semantics

    • Abstract: Publication date: Available online 6 November 2019Source: Annals of Pure and Applied LogicAuthor(s): Nebojša Ikodinović, Zoran Ognjanović, Aleksandar Perović, Miodrag Rašković We study propositional probabilistic logics (LPP–logics) with probability operators of the form P≥r (“the probability is at least r”) with σ–additive semantics. For regular infinite cardinals κ and λ, the probabilistic logic LPPκ,λ has λ propositional variables, allows conjunctions of
       
  • Elementary inductive dichotomy: Separation of open and clopen
           determinacies with infinite alternatives

    • Abstract: Publication date: Available online 4 November 2019Source: Annals of Pure and Applied LogicAuthor(s): Sato Kentaro We introduce a new axiom called inductive dichotomy, a weak variant of the axiom of inductive definition, and analyze the relationships with other variants of inductive definition and with related axioms, in the general second order framework, including second order arithmetic, second order set theory and higher order arithmetic. By applying these results to the investigations on the determinacy axioms, we show the following. (i) Clopen determinacy is consistency-wise strictly weaker than open determinacy in these frameworks, except second order arithmetic; this is an enhancement of Schweber–Hachtman separation of open and clopen determinacy into the consistency-wise separation. (ii) Hausdorff–Kuratowski hierarchy of differences of opens is faithfully reflected by the hierarchy of consistency strengths of corresponding parameter-free determinacies in the aforementioned frameworks; this result is valid also in second order arithmetic only except clopen determinacy.
       
  • Determinate Logic and the Axiom of Choice

    • Abstract: Publication date: Available online 7 October 2019Source: Annals of Pure and Applied LogicAuthor(s): J.P. Aguilera Takeuti introduced an infinitary proof system for determinate logic and showed that for transitive models of Zermelo-Fraenkel set theory with the Axiom of Dependent Choice that contain all reals, the cut-elimination theorem is equivalent to the Axiom of Determinacy, and in particular contradicts the Axiom of Choice.We consider variants of Takeuti's theorem without assuming the failure of the Axiom of Choice. For instance, we show that if one removes atomic formulae of infinite arity from the language of Takeuti's proof system, then cut elimination is equivalent to a determinacy hypothesis provable, e.g., in ZFC + “there are infinitely many Woodin cardinals.” A slight extension of the proof system admits cut elimination for countable sequents under the same assumptions.A simple modification of the proof system yields analogs of the results above for the Axiom of Real Determinacy and uncountably many Woodin cardinals.
       
  • Feasibly constructive proofs of succinct weak circuit lower bounds

    • Abstract: Publication date: Available online 10 September 2019Source: Annals of Pure and Applied LogicAuthor(s): Moritz Müller, Ján Pich We ask for feasibly constructive proofs of known circuit lower bounds for explicit functions on bit strings of length n. In 1995 Razborov showed that many can be proved in PV1, a bounded arithmetic formalizing polynomial time reasoning. He formalized circuit lower bound statements for small n of doubly logarithmic order. It is open whether PV1 proves known lower bounds in succinct formalizations for n of logarithmic order. We give such proofs in APC1, an extension of PV1 formalizing probabilistic polynomial time reasoning: for parity and AC0, for mod q and AC0[p] (only for n slightly smaller than logarithmic), and for k-clique and monotone circuits. We also formalize Razborov and Rudich's natural proof barrier.We ask for short propositional proofs of circuit lower bounds expressed succinctly by propositional formulas of size nO(1) or at least much smaller than the 2O(n) size of the common “truth table” formula. We discuss two such expressions: one via feasible functions witnessing errors of circuits, and one via the anticheckers of Lipton and Young 1994. Our APC1 formalizations yield conditional upper bounds for the succinct formulas obtained by witnessing: we get short Extended Frege proofs from general circuit lower bounds expressed by the common “truth-table” formulas. We also show how to construct in quasipolynomial time propositional proofs of quasipolynomial size tautologies expressing AC0[p] quasipolynomial size lower bounds; these proofs are in Jeřábek's system WF.
       
  • Remarks on generic stability in independent theories

    • Abstract: Publication date: Available online 5 September 2019Source: Annals of Pure and Applied LogicAuthor(s): Gabriel Conant, Kyle Gannon In NIP theories, generically stable Keisler measures can be characterized in several ways. We analyze these various forms of “generic stability” in arbitrary theories. Among other things, we show that the standard definition of generic stability for types coincides with the notion of a frequency interpretation measure. We also give combinatorial examples of types in NSOP theories that are finitely approximated but not generically stable, as well as ϕ-types in simple theories that are definable and finitely satisfiable in a small model, but not finitely approximated. Our proofs demonstrate interesting connections to classical results from Ramsey theory for finite graphs and hypergraphs.
       
  • Resolution over linear equations modulo two

    • Abstract: Publication date: Available online 21 August 2019Source: Annals of Pure and Applied LogicAuthor(s): Dmitry Itsykson, Dmitry Sokolov We consider an extension of the resolution proof system that operates with disjunctions of linear equalities over F2; we denote this system by Res(⊕). It is well known that tree-like resolution is equivalent in behaviour to DPLL algorithms for the Boolean satisfiability problem. Every DPLL algorithm splits the input problem into two by assigning two possible values to a variable; then it simplifies the two resulting formulas and makes two recursive calls. Tree-like Res(⊕)-proofs correspond to an extension of the DPLL paradigm, in which we can split by an arbitrary linear combination of variables modulo two. These algorithms quickly solve formulas that explicitly encode linear systems modulo two which were used for proving exponential lower bounds for conventional DPLL algorithms.We prove exponential lower bounds on the size of tree-like Res(⊕)-proofs. We also show that resolution and tree-like Res(⊕) do not simulate each other.We prove a space vs size tradeoff for Res(⊕)-proofs. We prove that Res(⊕) is implicationally complete and also that Res(⊕) is polynomially equivalent to its semantic version.We consider the proof system Res(⊕)[k] that is a restricted version of Res(⊕) operating with disjunctions of linear equalities such that at most k equalities depend on more than one variable. We simulate Res(⊕)[k] in the OBDD-based proof system with blowup 2k and in Polynomial Calculus Resolution with blowup 2nH(2k/n)poly(n), where n is the number of variables and H(p) is the binary entropy; the latter result implies exponential lower bounds on the size of Res(⊕)[δn]-proofs for some constant δ>0. Raz and Tzameret introduced the system R(lin) which operates with disjunctions of linear equalities with integer coefficients. We show that Res(⊕) can be p-simulated in R(lin).
       
  • Algebraic description of limit models in classes of abelian groups

    • Abstract: Publication date: Available online 21 August 2019Source: Annals of Pure and Applied LogicAuthor(s): Marcos Mazari-Armida We study limit models in the class of abelian groups with the subgroup relation and in the class of torsion-free abelian groups with the pure subgroup relation. We show: Theorem 0.1.(1)If G is a limit model of cardinality λ in the class of abelian groups with the subgroup relation, then G≅(⊕λQ)⊕⊕pprime(⊕λZ(p∞)).(2)If G is a limit model of cardinality λ in the class of torsion-free abelian groups with the pure subgroup relation, then:•If the length of the chain has uncountable cofinality, thenG≅(⊕λQ)⊕Πpprime(⊕λZ(p))‾.•If the length of the chain has countable cofinality, then G is not algebraically compact. We also study the class of finitely Butler groups with the pure subgroup relation, we show that it is an AEC, Galois-stable and (
       
  • Lyndon Interpolation Theorem of Instantial Neighborhood Logic -
           constructively via a sequent calculus

    • Abstract: Publication date: Available online 14 August 2019Source: Annals of Pure and Applied LogicAuthor(s): Junhua Yu Instantial neighborhood logic (INL) is classical propositional logic enriched by a two-sorted operator □. In a neighborhood model, a formula like □(α1,...,αj;α0) (for an arbitrary natural number j) means that, the current point has a neighborhood in which α0 universally holds and none of α1,...,αj universally fails. This paper offers to INL: (1) a cut-free sequent calculus, and (2) a constructive proof of its Lyndon interpolation theorem.
       
  • Decidability of the theory of modules over Prüfer domains with dense
           value groups

    • Abstract: Publication date: Available online 19 July 2019Source: Annals of Pure and Applied LogicAuthor(s): Lorna Gregory, Sonia L'Innocente, Carlo Toffalori We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains whose localizations at maximal ideals have dense value groups. For Bézout domains, these conditions are also necessary.
       
  • Supersimple ω-categorical theories and pregeometries

    • Abstract: Publication date: Available online 9 July 2019Source: Annals of Pure and Applied LogicAuthor(s): Vera Koponen We prove that if T is an ω-categorical supersimple theory with nontrivial dependence (given by forking), then there is a nontrivial regular 1-type over a finite set of reals which is realized by real elements; hence forking induces a nontrivial pregeometry on the solution set of this type and the pregeometry is definable (using only finitely many parameters). The assumption about ω-categoricity is necessary. This result is used to prove the following: If V is a finite relational vocabulary with maximal arity 3 and T is a supersimple V-theory with elimination of quantifiers, then T has trivial dependence and finite SU-rank. This immediately gives the following strengthening of [18, Theorem 4.1]: if M is a ternary simple homogeneous structure with only finitely many constraints, then Th(M) has trivial dependence and finite SU-rank.
       
  • Reductions between Types of Numberings

    • Abstract: Publication date: Available online 4 July 2019Source: Annals of Pure and Applied LogicAuthor(s): Ian Herbert, Sanjay Jain, Steffen Lempp, Mustafa Manat, Frank Stephan This paper considers reductions between types of numberings; these reductions preserve the Rogers Semilattice of the numberings reduced and also preserve the number of minimal and positive degrees in their semilattice. It is shown how to use these reductions to simplify some constructions of specific semilattices. Furthermore, it is shown that for the basic types of numberings, one can reduce the left-r.e. numberings to the r.e. numberings and the k-r.e. numberings to the (k+1)-r.e. numberings; all further reductions are obtained by concatenating these reductions.
       
  • Schmerl decompositions in first order arithmetic

    • Abstract: Publication date: Available online 4 July 2019Source: Annals of Pure and Applied LogicAuthor(s): François Dorais, Zachary Evans, Marcia Groszek, Seth Harris, Theodore Slaman Good m-tuples, m-tuples of r.e. sets without Schmerl decompositions, were introduced by Schmerl, who used them to investigate the reverse mathematics of Grundy colorings of graphs. Schmerl considered only standard m, for which our definitions of weakly good, good, and strongly good coincide. The existence of good tuples for nonstandard m depends on how much induction is available in the model. We show that in models of first-order arithmetic, over a base theory of IΔ10+BΣ10+EXP, the existence of arbitrarily long weakly good tuples is equivalent to IΣ10 and the existence of arbitrarily long good or strongly good tuples is equivalent to BΣ30. Consequences for second-order arithmetic include that, over RCA0⁎, the existence of arbitrarily long good tuples is equivalent to BΣ30+¬ACA.
       
  • Categories with families and first-order logic with dependent sorts

    • Abstract: Publication date: Available online 3 July 2019Source: Annals of Pure and Applied LogicAuthor(s): Erik Palmgren First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type theories. Categories with families (cwfs) is an established semantical structure for dependent type theories, such as Martin-Löf type theory. We introduce in this article a notion of hyperdoctrine over a cwf, and show how FOLDS and DFOL fit in this semantical framework. A soundness and completeness theorem is proved for DFOL. The semantics is functorial in the sense of Lawvere, and uses a dependent version of the Lindenbaum-Tarski algebra for a DFOL theory. Agreement with standard first-order semantics is established. Applications of DFOL to constructive mathematics and categorical foundations are given. A key feature is a local propositions-as-types principle.
       
 
 
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