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Showing 1 - 200 of 872 Journals sorted alphabetically
3D Printing and Additive Manufacturing     Full-text available via subscription   (Followers: 20)
Abakós     Open Access   (Followers: 4)
ACM Computing Surveys     Hybrid Journal   (Followers: 22)
ACM Journal on Computing and Cultural Heritage     Hybrid Journal   (Followers: 8)
ACM Journal on Emerging Technologies in Computing Systems     Hybrid Journal   (Followers: 11)
ACM Transactions on Accessible Computing (TACCESS)     Hybrid Journal   (Followers: 3)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Applied Perception (TAP)     Hybrid Journal   (Followers: 5)
ACM Transactions on Architecture and Code Optimization (TACO)     Hybrid Journal   (Followers: 9)
ACM Transactions on Autonomous and Adaptive Systems (TAAS)     Hybrid Journal   (Followers: 7)
ACM Transactions on Computation Theory (TOCT)     Hybrid Journal   (Followers: 12)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Computer Systems (TOCS)     Hybrid Journal   (Followers: 17)
ACM Transactions on Computer-Human Interaction     Hybrid Journal   (Followers: 14)
ACM Transactions on Computing Education (TOCE)     Hybrid Journal   (Followers: 5)
ACM Transactions on Design Automation of Electronic Systems (TODAES)     Hybrid Journal   (Followers: 3)
ACM Transactions on Economics and Computation     Hybrid Journal  
ACM Transactions on Embedded Computing Systems (TECS)     Hybrid Journal   (Followers: 3)
ACM Transactions on Information Systems (TOIS)     Hybrid Journal   (Followers: 19)
ACM Transactions on Intelligent Systems and Technology (TIST)     Hybrid Journal   (Followers: 7)
ACM Transactions on Interactive Intelligent Systems (TiiS)     Hybrid Journal   (Followers: 3)
ACM Transactions on Multimedia Computing, Communications, and Applications (TOMCCAP)     Hybrid Journal   (Followers: 9)
ACM Transactions on Reconfigurable Technology and Systems (TRETS)     Hybrid Journal   (Followers: 6)
ACM Transactions on Sensor Networks (TOSN)     Hybrid Journal   (Followers: 7)
ACM Transactions on Speech and Language Processing (TSLP)     Hybrid Journal   (Followers: 8)
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ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 27)
Acta Automatica Sinica     Full-text available via subscription   (Followers: 2)
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Advanced Engineering Materials     Hybrid Journal   (Followers: 28)
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AEU - International Journal of Electronics and Communications     Hybrid Journal   (Followers: 8)
African Journal of Information and Communication     Open Access   (Followers: 6)
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AI EDAM     Hybrid Journal  
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AIS Transactions on Human-Computer Interaction     Open Access   (Followers: 5)
Algebras and Representation Theory     Hybrid Journal   (Followers: 1)
Algorithms     Open Access   (Followers: 11)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Computational Mathematics     Open Access   (Followers: 4)
American Journal of Information Systems     Open Access   (Followers: 5)
American Journal of Sensor Technology     Open Access   (Followers: 4)
Anais da Academia Brasileira de Ciências     Open Access   (Followers: 2)
Analog Integrated Circuits and Signal Processing     Hybrid Journal   (Followers: 7)
Analysis in Theory and Applications     Hybrid Journal   (Followers: 1)
Animation Practice, Process & Production     Hybrid Journal   (Followers: 5)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
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Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of Software Engineering     Hybrid Journal   (Followers: 13)
Annual Reviews in Control     Hybrid Journal   (Followers: 6)
Anuario Americanista Europeo     Open Access  
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applied and Computational Harmonic Analysis     Full-text available via subscription   (Followers: 1)
Applied Artificial Intelligence: An International Journal     Hybrid Journal   (Followers: 13)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Clinical Informatics     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Computer Systems     Open Access   (Followers: 2)
Applied Informatics     Open Access  
Applied Mathematics and Computation     Hybrid Journal   (Followers: 33)
Applied Medical Informatics     Open Access   (Followers: 10)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Soft Computing     Hybrid Journal   (Followers: 16)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
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Architectural Theory Review     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives and Museum Informatics     Hybrid Journal   (Followers: 132)
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
arq: Architectural Research Quarterly     Hybrid Journal   (Followers: 7)
Artifact     Hybrid Journal   (Followers: 2)
Artificial Life     Hybrid Journal   (Followers: 7)
Asia Pacific Journal on Computational Engineering     Open Access  
Asia-Pacific Journal of Information Technology and Multimedia     Open Access   (Followers: 1)
Asian Journal of Computer Science and Information Technology     Open Access  
Asian Journal of Control     Hybrid Journal  
Assembly Automation     Hybrid Journal   (Followers: 2)
at - Automatisierungstechnik     Hybrid Journal   (Followers: 1)
Australian Educational Computing     Open Access   (Followers: 1)
Automatic Control and Computer Sciences     Hybrid Journal   (Followers: 4)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Automatica     Hybrid Journal   (Followers: 11)
Automation in Construction     Hybrid Journal   (Followers: 6)
Autonomous Mental Development, IEEE Transactions on     Hybrid Journal   (Followers: 9)
Basin Research     Hybrid Journal   (Followers: 5)
Behaviour & Information Technology     Hybrid Journal   (Followers: 52)
Big Data and Cognitive Computing     Open Access   (Followers: 2)
Biodiversity Information Science and Standards     Open Access  
Bioinformatics     Hybrid Journal   (Followers: 283)
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Biomedical Engineering and Computational Biology     Open Access   (Followers: 13)
Biomedical Engineering, IEEE Reviews in     Full-text available via subscription   (Followers: 19)
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Briefings in Bioinformatics     Hybrid Journal   (Followers: 43)
British Journal of Educational Technology     Hybrid Journal   (Followers: 144)
Broadcasting, IEEE Transactions on     Hybrid Journal   (Followers: 10)
c't Magazin fuer Computertechnik     Full-text available via subscription   (Followers: 1)
CALCOLO     Hybrid Journal  
Calphad     Hybrid Journal  
Canadian Journal of Electrical and Computer Engineering     Full-text available via subscription   (Followers: 14)
Capturing Intelligence     Full-text available via subscription  
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
Cell Communication and Signaling     Open Access   (Followers: 2)
Central European Journal of Computer Science     Hybrid Journal   (Followers: 5)
CERN IdeaSquare Journal of Experimental Innovation     Open Access   (Followers: 2)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chemometrics and Intelligent Laboratory Systems     Hybrid Journal   (Followers: 14)
ChemSusChem     Hybrid Journal   (Followers: 7)
China Communications     Full-text available via subscription   (Followers: 7)
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
CIN Computers Informatics Nursing     Full-text available via subscription   (Followers: 11)
Circuits and Systems     Open Access   (Followers: 15)
Clean Air Journal     Full-text available via subscription   (Followers: 1)
CLEI Electronic Journal     Open Access  
Clin-Alert     Hybrid Journal   (Followers: 1)
Cluster Computing     Hybrid Journal   (Followers: 1)
Cognitive Computation     Hybrid Journal   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Communication Methods and Measures     Hybrid Journal   (Followers: 12)
Communication Theory     Hybrid Journal   (Followers: 20)
Communications Engineer     Hybrid Journal   (Followers: 1)
Communications in Algebra     Hybrid Journal   (Followers: 3)
Communications in Computational Physics     Full-text available via subscription   (Followers: 2)
Communications in Partial Differential Equations     Hybrid Journal   (Followers: 3)
Communications of the ACM     Full-text available via subscription   (Followers: 52)
Communications of the Association for Information Systems     Open Access   (Followers: 16)
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering     Hybrid Journal   (Followers: 3)
Complex & Intelligent Systems     Open Access   (Followers: 1)
Complex Adaptive Systems Modeling     Open Access  
Complex Analysis and Operator Theory     Hybrid Journal   (Followers: 2)
Complexity     Hybrid Journal   (Followers: 6)
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Computación y Sistemas     Open Access  
Computation     Open Access  
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 and Structural Biotechnology Journal     Open Access   (Followers: 2)
Computational and Theoretical Chemistry     Hybrid Journal   (Followers: 9)
Computational Astrophysics and Cosmology     Open Access   (Followers: 1)
Computational Biology and Chemistry     Hybrid Journal   (Followers: 11)
Computational Chemistry     Open Access   (Followers: 2)
Computational Cognitive Science     Open Access   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Condensed Matter     Open Access  
Computational Ecology and Software     Open Access   (Followers: 9)
Computational Economics     Hybrid Journal   (Followers: 9)
Computational Geosciences     Hybrid Journal   (Followers: 15)
Computational Linguistics     Open Access   (Followers: 23)
Computational Management Science     Hybrid Journal  
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Molecular Bioscience     Open Access   (Followers: 2)
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computational Particle Mechanics     Hybrid Journal   (Followers: 1)
Computational Research     Open Access   (Followers: 1)
Computational Science and Discovery     Full-text available via subscription   (Followers: 2)
Computational Science and Techniques     Open Access  
Computational Statistics     Hybrid Journal   (Followers: 14)
Computational Statistics & Data Analysis     Hybrid Journal   (Followers: 30)
Computer     Full-text available via subscription   (Followers: 94)
Computer Aided Surgery     Hybrid Journal   (Followers: 6)
Computer Applications in Engineering Education     Hybrid Journal   (Followers: 8)
Computer Communications     Hybrid Journal   (Followers: 10)
Computer Engineering and Applications Journal     Open Access   (Followers: 5)
Computer Journal     Hybrid Journal   (Followers: 9)
Computer Methods in Applied Mechanics and Engineering     Hybrid Journal   (Followers: 23)
Computer Methods in Biomechanics and Biomedical Engineering     Hybrid Journal   (Followers: 12)
Computer Methods in the Geosciences     Full-text available via subscription   (Followers: 2)
Computer Music Journal     Hybrid Journal   (Followers: 19)

        1 2 3 4 5 6 | Last

Journal Cover Annals of Pure and Applied Logic
  [SJR: 1.19]   [H-I: 33]   [2 followers]  Follow
  This is an Open Access Journal Open Access journal
   ISSN (Print) 0168-0072
   Published by Elsevier Homepage  [3175 journals]
  • Topology and measure in logics for region-based theories of space

    • Authors: Tamar Lando
      Pages: 277 - 311
      Abstract: Publication date: Available online 3 January 2018
      Source:Annals of Pure and Applied Logic
      Author(s): Tamar Lando
      Space, as we typically represent it in mathematics and physics, is composed of dimensionless, indivisible points. On an alternative, region-based approach to space, extended regions together with the relations of ‘parthood’ and ‘contact’ are taken as primitive; points are represented as mathematical abstractions from regions. Region-based theories of space have been traditionally modeled in regular closed (or regular open) algebras, in work that goes back to [5] and [20]. More recently, formal logics for region-based theories of space were developed in, e.g., [3] and [18]. It was shown that these logics have both a nice topological and relational semantics, and that the minimal logic for contact algebras, L m i n c o n t (defined below), is complete for both. The present paper explores the question of completeness of L m i n c o n t and its extensions for individual topological spaces of interest: the real line, Cantor space, the rationals, and the infinite binary tree. A second aim is to study a different, algebraic model of logics for region-based theories of space, based on the Lebesgue measure algebra (or algebra of Borel subsets of the real line modulo sets of Lebesgue measure zero). As a model for point-free space, the algebra was first discussed in [2]. The main results of the paper are that L m i n c o n t is weakly complete for any zero-dimensional, dense-in-itself metric space (including, e.g., Cantor space and the rationals); the extension L m i n c o n t + ( C o n ) is weakly complete for the real line and the Lebesgue measure contact algebra. We also prove that the logic L m i n c o n t + ( U n i v ) is weakly complete for the infinite binary tree.

      PubDate: 2018-01-10T11:03:22Z
      DOI: 10.1016/j.apal.2017.12.002
      Issue No: Vol. 169, No. 4 (2018)
  • Density of the cototal enumeration degrees

    • Authors: Joseph S. Miller; Mariya I. Soskova
      Abstract: Publication date: Available online 8 January 2018
      Source:Annals of Pure and Applied Logic
      Author(s): Joseph S. Miller, Mariya I. Soskova
      We prove that the cototal enumeration degrees are exactly the enumeration degrees of sets with good approximations, as introduced by Lachlan and Shore [17]. Good approximations have been used as a tool to prove density results in the enumerations degrees, and indeed, we prove that the cototal enumerations degrees are dense.

      PubDate: 2018-01-10T11:03:22Z
      DOI: 10.1016/j.apal.2018.01.001
  • Structure and enumeration theorems for hereditary properties in finite
           relational languages

    • Authors: Terry
      Abstract: Publication date: Available online 8 January 2018
      Source:Annals of Pure and Applied Logic
      Author(s): C. Terry
      Given a finite relational language L , a hereditary L -property is a class of finite L -structures which is closed under isomorphism and model theoretic substructure. This notion encompasses many objects of study in extremal combinatorics, including (but not limited to) hereditary properties of graphs, hypergraphs, and oriented graphs. In this paper, we generalize certain definitions, tools, and results form the study of hereditary properties in combinatorics to the setting of hereditary L -properties, where L is any finite relational language with maximum arity at least two. In particular, the goal of this paper is to generalize how extremal results and stability theorems can be combined with well-known techniques and tools to yield approximate enumeration and structure theorems. We accomplish this by generalizing the notions of extremal graphs, asymptotic density, and graph stability theorems using structures in an auxiliary language associated to a hereditary L -property. Given a hereditary L -property H , we prove an approximate asymptotic enumeration theorem for H in terms of its generalized asymptotic density. Further we prove an approximate structure theorem for H , under the assumption of that H has a stability theorem. The tools we use include a new application of the hypergraph containers theorem (Balogh-Morris-Samotij [14], Saxton-Thomason [38]) to the setting of L -structures, a general supersaturation theorem for hereditary L -properties (also new), and a general graph removal lemma for L -structures proved by Aroskar and Cummings in [5]. Similar results in the setting of multicolored graphs and hypergraphs were recently proved independently by Falgas-Ravry, O'Connel, Strömberg, and Uzzell [21].

      PubDate: 2018-01-10T11:03:22Z
  • No finite axiomatizations for posets embeddable into distributive lattices

    • Authors: Rob Egrot
      Pages: 235 - 242
      Abstract: Publication date: March 2018
      Source:Annals of Pure and Applied Logic, Volume 169, Issue 3
      Author(s): Rob Egrot
      Let m and n be cardinals with 3 ≤ m , n ≤ ω . We show that the class of posets that can be embedded into a distributive lattice via a map preserving all existing meets and joins with cardinalities strictly less than m and n respectively cannot be finitely axiomatized.

      PubDate: 2017-12-26T15:48:58Z
      DOI: 10.1016/j.apal.2017.11.001
  • Jumps of computably enumerable equivalence relations

    • Authors: Uri Andrews; Andrea Sorbi
      Pages: 243 - 259
      Abstract: Publication date: March 2018
      Source:Annals of Pure and Applied Logic, Volume 169, Issue 3
      Author(s): Uri Andrews, Andrea Sorbi
      We study computably enumerable equivalence relations (or, ceers), under computable reducibility ≤, and the halting jump operation on ceers. We show that every jump is uniform join-irreducible, and thus join-irreducible. Therefore, the uniform join of two incomparable ceers is not equivalent to any jump. On the other hand there exist ceers that are not equivalent to jumps, but are uniform join-irreducible: in fact above any non-universal ceer there is a ceer which is not equivalent to a jump, and is uniform join-irreducible. We also study transfinite iterations of the jump operation. If a is an ordinal notation, and E is a ceer, then let E ( a ) denote the ceer obtained by transfinitely iterating the jump on E along the path of ordinal notations up to a. In contrast with what happens for the Turing jump and Turing reducibility, where if a set X is an upper bound for the A-arithmetical sets then X ( 2 ) computes A ( ω ) , we show that there is a ceer R such that R ≥ Id ( n ) , for every finite ordinal n, but, for all k, R ( k ) ≱ Id ( ω ) (here Id is the identity equivalence relation). We show that if a , b are notations of the same ordinal less than ω 2 , then E ( a ) ≡ E ( b ) , but there are notations a , b of ω 2 such that Id ( a ) and Id ( b ) are incomparable. Moreover, there is no non-universal ceer which is an upper bound for all the ceers of the form Id ( a ) where a is a notation for ω 2 .

      PubDate: 2017-12-26T15:48:58Z
      DOI: 10.1016/j.apal.2017.12.001
  • Full-splitting Miller trees and infinitely often equal reals

    • Authors: Yurii Khomskii; Giorgio Laguzzi
      Pages: 1491 - 1506
      Abstract: Publication date: August 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 8
      Author(s): Yurii Khomskii, Giorgio Laguzzi
      We investigate two closely related partial orders of trees on ω ω : the full-splitting Miller trees and the infinitely often equal trees, as well as their corresponding σ-ideals. The former notion was considered by Newelski and Rosłanowski while the latter involves a correction of a result of Spinas. We consider some Marczewski-style regularity properties based on these trees, which turn out to be closely related to the property of Baire, and look at the dichotomies of Newelski–Rosłanowski and Spinas for higher projective pointclasses. We also provide some insight concerning a question of Fremlin whether one can add an infinitely often equal real without adding a Cohen real, which was recently solved by Zapletal.

      PubDate: 2017-05-21T15:55:03Z
      DOI: 10.1016/j.apal.2017.02.001
  • On the decidability of the theory of modules over the ring of algebraic

    • Authors: Sonia L'Innocente; Carlo Toffalori; Gena Puninski
      Pages: 1507 - 1516
      Abstract: Publication date: August 2017
      Source:Annals of Pure and Applied Logic, Volume 168, Issue 8
      Author(s): Sonia L'Innocente, Carlo Toffalori, Gena Puninski
      We will prove that the theory of all modules over the ring of algebraic integers is decidable.

      PubDate: 2017-05-21T15:55:03Z
      DOI: 10.1016/j.apal.2017.02.003
  • Proof lengths for instances of the Paris–Harrington principle

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

      PubDate: 2017-05-01T14:19:49Z
      DOI: 10.1016/j.apal.2017.01.004
  • Tarski's Theorem on Intuitionistic Logic, for Polyhedra

    • Authors: Nick Bezhanishvili; Vincenzo Marra; Daniel McNeill; Andrea Pedrini
      Abstract: Publication date: Available online 17 December 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Nick Bezhanishvili, Vincenzo Marra, Daniel McNeill, Andrea Pedrini
      In 1938, Tarski proved that a formula is not intuitionistically valid if, and only if, it has a counter-model in the Heyting algebra of open sets of some topological space. In fact, Tarski showed that any Euclidean space R n with n ⩾ 1 suffices, as does e.g. the Cantor space. In particular, intuitionistic logic cannot detect topological dimension in the Heyting algebra of all open sets of a Euclidean space. By contrast, we consider the lattice of open subpolyhedra of a given compact polyhedron P ⊆ R n , prove that it is a locally finite Heyting subalgebra of the (non-locally-finite) algebra of all open sets of P, and show that intuitionistic logic is able to capture the topological dimension of P through the bounded-depth axiom schemata. Further, we show that intuitionistic logic is precisely the logic of formulæ valid in all Heyting algebras arising from polyhedra in this manner. Thus, our main theorem reconciles through polyhedral geometry two classical results: topological completeness in the style of Tarski, and Jaśkowski's theorem that intuitionistic logic enjoys the finite model property. Several questions of interest remain open. E.g., what is the intermediate logic of all closed triangulable manifolds'

      PubDate: 2017-12-26T15:48:58Z
      DOI: 10.1016/j.apal.2017.12.005
  • The omega-rule interpretation of transfinite provability logic

    • Authors: David Fernández-Duque; Joost J. Joosten
      Abstract: Publication date: Available online 14 December 2017
      Source:Annals of Pure and Applied Logic
      Author(s): David Fernández-Duque, Joost J. Joosten
      Given a computable ordinal Λ, the transfinite provability logic GLP Λ has for each ξ < Λ a modality [ ξ ] intended to represent a provability predicate within a chain of increasing strength. One possibility is to read [ ξ ] ϕ as ϕ is provable in T using ω-rules of depth at most ξ, where T is a second-order theory extending ACA 0 . In this paper we will formalize such iterations of ω-rules in second-order arithmetic and show how it is a special case of what we call uniform provability predicates. Uniform provability predicates are similar to Ignatiev's strong provability predicates except that they can be iterated transfinitely. Finally, we show that GLP Λ is sound and complete for any uniform provability predicate.

      PubDate: 2017-12-26T15:48:58Z
      DOI: 10.1016/j.apal.2017.12.006
  • Recognizable sets and Woodin cardinals: computation beyond the
           constructible universe

    • Authors: Merlin Carl; Philipp Schlicht; Philip Welch
      Abstract: Publication date: Available online 13 December 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Merlin Carl, Philipp Schlicht, Philip Welch
      We call a subset of an ordinal λ recognizable if it is the unique subset x of λ for which some Turing machine with ordinal time and tape and an ordinal parameter, that halts for all subsets of λ as input, halts with the final state 0. Equivalently, such a set is the unique subset x which satisfies a given Σ 1 formula in L [ x ] . We further define the recognizable closure for subsets of λ by closing under relative recognizability for subsets of λ. We prove several results about recognizable sets and their variants for other types of machines. Notably, we show the following results from large cardinals. • Recognizable sets of ordinals appear in the hierarchy of inner models at least up to the level Woodin cardinals, while computable sets are elements of L. • A subset of a countable ordinal λ is in the recognizable closure for subsets of λ if and only if it is an element of the inner model M ∞ , which is obtained by iterating the least measure of the least fine structural inner model M 1 with a Woodin cardinal through the ordinals.

      PubDate: 2017-12-26T15:48:58Z
      DOI: 10.1016/j.apal.2017.12.007
  • Intuitionistic nonstandard bounded modified realisability and functional

    • Authors: Bruno Dinis; Jaime Gaspar
      Abstract: Publication date: Available online 12 December 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Bruno Dinis, Jaime Gaspar
      We present a bounded modified realisability and a bounded functional interpretation of intuitionistic nonstandard arithmetic with nonstandard principles. The functional interpretation is the intuitionistic counterpart of Ferreira and Gaspar's functional interpretation and has similarities with Van den Berg, Briseid and Safarik's functional interpretation but replacing finiteness by majorisability. We give a threefold contribution: constructive content and proof-theoretical properties of nonstandard arithmetic; filling a gap in the literature; being in line with nonstandard methods to analyse compactness arguments.

      PubDate: 2017-12-26T15:48:58Z
      DOI: 10.1016/j.apal.2017.12.004
  • Martin-Löf random generalized Poisson processes

    • Authors: Logan Axon
      Abstract: Publication date: Available online 8 December 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Logan Axon
      Martin-Löf randomness was originally defined and studied in the context of the Cantor space 2 ω . In [1] probability theoretic random closed sets (RACS) are used as the foundation for the study of Martin-Löf randomness in spaces of closed sets. We use that framework to explore Martin-Löf randomness for the space of closed subsets of R and a particular family of measures on this space, the generalized Poisson processes. This gives a novel class of Martin-Löf random closed subsets of R . We describe some of the properties of these Martin-Löf random closed sets; one result establishes that a real number is Martin-Löf random if and only if it is contained in some Martin-Löf random closed set.

      PubDate: 2017-12-26T15:48:58Z
      DOI: 10.1016/j.apal.2017.12.003
  • An analysis of the logic of Riesz spaces with strong unit

    • Authors: Antonio Di Nola; Serafina Lapenta; Ioana Leuştean
      Abstract: Publication date: Available online 31 October 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Antonio Di Nola, Serafina Lapenta, Ioana Leuştean
      We study Łukasiewicz logic enriched by a scalar multiplication with scalars in [ 0 , 1 ] . Its algebraic models, called Riesz MV-algebras, are, up to isomorphism, unit intervals of Riesz spaces with strong unit endowed with an appropriate structure. When only rational scalars are considered, one gets the class of DMV-algebras and a corresponding logical system. Our research follows two objectives. The first one is to deepen the connections between functional analysis and the logic of Riesz MV-algebras. The second one is to study the finitely presented MV-algebras, DMV-algebras and Riesz MV-algebras, connecting them from logical, algebraic and geometric perspective.

      PubDate: 2017-11-01T20:48:41Z
      DOI: 10.1016/j.apal.2017.10.006
  • Capturing k-ary existential second order logic with k-ary
           inclusion–exclusion logic

    • Authors: Raine
      Abstract: Publication date: Available online 20 October 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Raine Rönnholm
      In this paper we analyze k-ary inclusion–exclusion logic, INEX[k], which is obtained by extending first order logic with k-ary inclusion and exclusion atoms. We show that every formula of INEX[k] can be expressed with a formula of k-ary existential second order logic, ESO[k]. Conversely, every formula of ESO[k] with at most k-ary free relation variables can be expressed with a formula of INEX[k]. From this it follows that, on the level of sentences, INEX[k] captures the expressive power of ESO[k]. We also introduce several useful operators that can be expressed in INEX[k]. In particular, we define inclusion and exclusion quantifiers and so-called term value preserving disjunction which is essential for the proofs of the main results in this paper. Furthermore, we present a novel method of relativization for team semantics and analyze the duality of inclusion and exclusion atoms.

      PubDate: 2017-10-25T18:02:37Z
  • Determinacy of refinements to the difference hierarchy of co-analytic sets

    • Authors: Chris Le Sueur
      Abstract: Publication date: Available online 17 October 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Chris Le Sueur
      In this paper we develop a technique for proving determinacy of classes of the form ω 2 - Π 1 1 + Γ (a refinement of the difference hierarchy on Π 1 1 lying between ω 2 - Π 1 1 and ( ω 2 + 1 ) - Π 1 1 ) from weak principles, establishing upper bounds for the determinacy-strength of the classes ω 2 - Π 1 1 + Σ α 0 for all computable α and of ω 2 - Π 1 1 + Δ 1 1 . This bridges the gap between previously known hypotheses implying determinacy in this region.

      PubDate: 2017-10-25T18:02:37Z
      DOI: 10.1016/j.apal.2017.10.001
  • Beyond abstract elementary classes: On the model theory of geometric

    • Authors: Tapani Hyttinen; Gianluca Paolini
      Abstract: Publication date: Available online 17 October 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Tapani Hyttinen, Gianluca Paolini
      Based on Crapo's theory of one point extensions of combinatorial geometries, we find various classes of geometric lattices that behave very well from the point of view of stability theory. One of them, ( K 3 , ≼ ) , is ω-stable, it has a monster model and an independence calculus that satisfies all the usual properties of non-forking. On the other hand, these classes are rather unusual, e.g. in ( K 3 , ≼ ) the Smoothness Axiom fails, and so ( K 3 , ≼ ) is not an AEC.

      PubDate: 2017-10-25T18:02:37Z
      DOI: 10.1016/j.apal.2017.10.003
  • The tree property at double successors of singular cardinals of
           uncountable cofinality

    • Authors: Mohammad Golshani; Rahman Mohammadpour
      Abstract: Publication date: Available online 14 October 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Mohammad Golshani, Rahman Mohammadpour
      Assuming the existence of a strong cardinal κ and a measurable cardinal above it, we force a generic extension in which κ is a singular strong limit cardinal of any given cofinality, and such that the tree property holds at κ + + .

      PubDate: 2017-10-25T18:02:37Z
      DOI: 10.1016/j.apal.2017.10.004
  • Wild theories with o-minimal open core

    • Authors: Philipp Hieronymi; Travis Nell; Erik Walsberg
      Abstract: Publication date: Available online 13 October 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Philipp Hieronymi, Travis Nell, Erik Walsberg
      Let T be a consistent o-minimal theory extending the theory of densely ordered groups and let T ′ be a consistent theory. Then there is a complete theory T ⁎ extending T such that T is an open core of T ⁎ , but every model of T ⁎ interprets a model of T ′ . If T ′ is NIP, T ⁎ can be chosen to be NIP as well. From this we deduce the existence of an NIP expansion of the real field that has no distal expansion.

      PubDate: 2017-10-13T17:01:42Z
      DOI: 10.1016/j.apal.2017.10.002
  • Pure patterns of order 2

    • Authors: Gunnar Wilken
      Abstract: Publication date: Available online 21 September 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Gunnar Wilken
      We provide mutual elementary recursive order isomorphisms between classical ordinal notations, based on Skolem hulling, and notations from pure elementary patterns of resemblance of order 2, showing that the latter characterize the proof-theoretic ordinal 1 ∞ of the fragment Π 1 1 – CA 0 of second order number theory, or equivalently the set theory KP ℓ 0 . As a corollary, we prove that Carlson's result on the well-quasi orderedness of respecting forests of order 2 implies transfinite induction up to the ordinal 1 ∞ . We expect that our approach will facilitate analysis of more powerful systems of patterns.

      PubDate: 2017-09-25T15:43:37Z
      DOI: 10.1016/j.apal.2017.09.001
  • Corrigendum to “The d.r.e. degrees are not dense” [Ann. Pure Appl.
           Logic 55 (1991) 125–151]

    • Authors: S. Barry Cooper; Leo Harrington; Alistair H. Lachlan; Steffen Lempp; Robert I. Soare
      Abstract: Publication date: Available online 31 July 2017
      Source:Annals of Pure and Applied Logic
      Author(s): S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp, Robert I. Soare
      We indicate how to fix an error in the proof of the main theorem of our original paper, pointed out to us by Yong Liu and Keng Meng Ng.

      PubDate: 2017-08-02T20:59:43Z
      DOI: 10.1016/j.apal.2017.07.001
  • Direct twisted Galois stratification

    • Authors: Ivan
      Abstract: Publication date: Available online 26 July 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Ivan Tomašić
      The theory ACFA admits a primitive recursive quantifier elimination procedure. It is therefore primitive recursively decidable.

      PubDate: 2017-08-02T20:59:43Z
  • A computational glimpse at the Leibniz and Frege hierarchies

    • Authors: Tommaso Moraschini
      Abstract: Publication date: Available online 26 July 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Tommaso Moraschini
      In this paper we consider, from a computational point of view, the problem of classifying logics within the Leibniz and Frege hierarchies typical of abstract algebraic logic. The main result states that, for logics presented syntactically, this problem is in general undecidable. More precisely, we show that there is no algorithm that classifies the logic of a finite consistent Hilbert calculus in the Leibniz and in the Frege hierarchies.

      PubDate: 2017-08-02T20:59:43Z
      DOI: 10.1016/j.apal.2017.07.003
  • The Lascar groups and the first homology groups in model theory

    • Authors: Jan Dobrowolski; Byunghan Kim; Junguk Lee
      Abstract: Publication date: Available online 4 July 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Jan Dobrowolski, Byunghan Kim, Junguk Lee
      Let p be a strong type of an algebraically closed tuple over B = acl eq ( B ) in any theory T. Depending on a ternary relation Image 1 satisfying some basic axioms (there is at least one such, namely the trivial independence in T), the first homology group H 1 ⁎ ( p ) can be introduced, similarly to [3]. We show that there is a canonical surjective homomorphism from the Lascar group over B to H 1 ⁎ ( p ) . We also notice that the map factors naturally via a surjection from the ‘relativised’ Lascar group of the type (which we define in analogy with the Lascar group of the theory) onto the homology group, and we give an explicit description of its kernel. Due to this characterization, it follows that the first homology group of p is independent from the choice of Image 1 , and can be written simply as H 1 ( p ) . As consequences, in any T, we show that H 1 ( p ) ≥ 2 ℵ 0 unless H 1 ( p ) is trivial, and we give a criterion for the equality of stp and Lstp of algebraically closed tuples using the notions of the first homology group and a relativised Lascar group. We also argue how any abelian connected compact group can appear as the first homology group of the type of a model.

      PubDate: 2017-07-09T19:02:42Z
      DOI: 10.1016/j.apal.2017.06.006
  • Orbits of subsets of the monster model and geometric theories

    • Authors: Enrique Casanovas; Luis Jaime Corredor
      Abstract: Publication date: Available online 30 June 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Enrique Casanovas, Luis Jaime Corredor
      Let M be the monster model of a complete first-order theory T. If D is a subset of M , following D. Zambella we consider e ( D ) = { D ′ ( M , D ) ≡ ( M , D ′ ) } and o ( D ) = { D ′ ( M , D ) ≅ ( M , D ′ ) } . The general question we ask is when e ( D ) = o ( D ) ' The case where D is A-invariant for some small set A is rather straightforward: it just means that D is definable. We investigate the case where D is not invariant over any small subset. If T is geometric and ( M , D ) is an H-structure (in the sense of A. Berenstein and E. Vassiliev) we get some answers. In the case of SU-rank one, e ( D ) is always different from o ( D ) . In the o-minimal case, everything can happen, depending on the complexity of the definable closure. We also study the case of lovely pairs of geometric theories.

      PubDate: 2017-07-09T19:02:42Z
      DOI: 10.1016/j.apal.2017.06.005
  • Monadic second-order properties of very sparse random graphs

    • Authors: L.B. Ostrovsky; M.E. Zhukovskii
      Abstract: Publication date: Available online 21 June 2017
      Source:Annals of Pure and Applied Logic
      Author(s): L.B. Ostrovsky, M.E. Zhukovskii
      We study asymptotical probabilities of first order and monadic second order properties of Bernoulli random graph G ( n , n − a ) . The random graph obeys FO (MSO) zero-one k-law (k is a positive integer) if, for any first order (monadic second order) formulae with quantifier depth at most k, it is true for G ( n , n − a ) with probability tending to 0 or to 1. Zero-one k-laws are well studied only for the first order language and a < 1 . We obtain new zero-one k-laws (both for first order and monadic second order languages) when a > 1 . Proofs of these results are based on the earlier studies of first order equivalence classes and our study of monadic second order equivalence classes. The respective results are of interest by themselves.

      PubDate: 2017-06-28T18:34:50Z
      DOI: 10.1016/j.apal.2017.06.004
  • Slow Reflection

    • Authors: Anton Freund
      Abstract: Publication date: Available online 20 June 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Anton Freund
      We describe a “slow” version of the hierarchy of uniform reflection principles over Peano Arithmetic (PA). These principles are unprovable in Peano Arithmetic (even when extended by usual reflection principles of lower complexity) and introduce a new provably total function. At the same time the consistency of PA plus slow reflection is provable in PA + Con ( PA ) . We deduce a conjecture of S.-D. Friedman, Rathjen and Weiermann: Transfinite iterations of slow consistency generate a hierarchy of precisely ε 0 stages between PA and PA + Con ( PA ) (where Con ( PA ) refers to the usual consistency statement).

      PubDate: 2017-06-28T18:34:50Z
      DOI: 10.1016/j.apal.2017.06.003
  • Clustered cell decomposition in P-minimal structures

    • Authors: Saskia Chambille; Pablo Cubides Kovacsics; Eva Leenknegt
      Abstract: Publication date: Available online 9 June 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Saskia Chambille, Pablo Cubides Kovacsics, Eva Leenknegt
      We prove that in a P-minimal structure, every definable set can be partitioned as a finite union of classical cells and regular clustered cells. This is a generalization of previously known cell decomposition results by Denef and Mourgues, which were dependent on the existence of definable Skolem functions. Clustered cells have the same geometric structure as classical, Denef-type cells, but do not have a definable function as center. Instead, the center is given by a definable set whose fibers are finite unions of balls.

      PubDate: 2017-06-10T17:06:33Z
      DOI: 10.1016/j.apal.2017.06.002
  • A microscopic approach to Souslin-tree constructions. Part I

    • Authors: Ari Meir Brodsky; Assaf Rinot
      Abstract: Publication date: Available online 8 June 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Ari Meir Brodsky, Assaf Rinot
      We propose a parameterized proxy principle from which κ-Souslin trees with various additional features can be constructed, regardless of the identity of κ. We then introduce the microscopic approach, which is a simple method for deriving trees from instances of the proxy principle. As a demonstration, we give a construction of a coherent κ-Souslin tree that applies also for κ inaccessible. We then carry out a systematic study of the consistency of instances of the proxy principle, distinguished by the vector of parameters serving as its input. Among other things, it will be shown that all known ⋄-based constructions of κ-Souslin trees may be redirected through this new proxy principle.

      PubDate: 2017-06-10T17:06:33Z
      DOI: 10.1016/j.apal.2017.05.003
  • Ramsey type properties of ideals

    • Abstract: Publication date: Available online 7 June 2017
      Source:Annals of Pure and Applied Logic
      Author(s): M. Hrušák, D. Meza-Alcántara, E. Thümmel, C. Uzcátegui
      We study several combinatorial properties of (mostly definable) ideals on countable sets. In several cases, we identify critical ideals for such properties in the Katětov order. In particular, the ideal R generated by the homogeneous subsets of the random graph is critical for the Ramsey property. The question as to whether there is a tall definable Ramsey ideal is raised and studied. It is shown that no tall F σ ideal is Ramsey, while there is a tall co-analytic Ramsey ideal.

      PubDate: 2017-06-10T17:06:33Z
  • Increasing sentences in Simple Type Theory

    • Authors: Panagiotis Rouvelas
      Abstract: Publication date: Available online 26 May 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Panagiotis Rouvelas
      We introduce the notion of pseudo-increasing sentence, and prove that all such sentences are decidable by a weak subtheory of Simple Type Theory with infinitely many zero-type elements. We then present the consequences of this result to Quine's theory of “New Foundations” (NF). In particular, we prove the decidability of certain universal-existential sentences, and establish the consistency of a subtheory of NF.

      PubDate: 2017-06-01T16:29:34Z
      DOI: 10.1016/j.apal.2017.05.002
  • Uniform interpolation and compact congruences

    • Authors: Samuel van; Gool George Metcalfe Constantine Tsinakis
      Abstract: Publication date: Available online 26 May 2017
      Source:Annals of Pure and Applied Logic
      Author(s): Samuel J. van Gool, George Metcalfe, Constantine Tsinakis
      Uniform interpolation properties are defined for equational consequence in a variety of algebras and related to properties of compact congruences on first the free and then the finitely presented algebras of the variety. It is also shown, following related results of Ghilardi and Zawadowski, that a combination of these properties provides a sufficient condition for the first-order theory of the variety to admit a model completion.

      PubDate: 2017-05-26T16:09:09Z
  • Universal graphs at ℵω1+1

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

      PubDate: 2017-05-07T14:48:17Z
      DOI: 10.1016/j.apal.2017.04.005
  • Addendum to: “The Bolzano–Weierstrass theorem is the jump of weak
           Kőnig's lemma” [Ann. Pure Appl. Logic 163 (6) (2012) 623–655]

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

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

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

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

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

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

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

      PubDate: 2017-04-09T20:53:23Z
      DOI: 10.1016/j.apal.2017.04.001
  • Abelian C-minimal valued groups

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

      PubDate: 2017-04-02T17:28:22Z
      DOI: 10.1016/j.apal.2017.03.008
  • Shelah's eventual categoricity conjecture in universal classes: Part I

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

      PubDate: 2017-04-02T17:28:22Z
      DOI: 10.1016/j.apal.2017.03.003
  • Homology groups of types in stable theories and the Hurewicz

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      PubDate: 2017-03-02T08:54:36Z
      DOI: 10.1016/j.apal.2017.02.005
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