Year:

  1.  4
    Diagonal Supercompact Radin Forcing.Omer Ben-Neria, Chris Lambie-Hanson & Spencer Unger - 2020 - Annals of Pure and Applied Logic 171 (10):102828.
    Motivated by the goal of constructing a model in which there are no κ-Aronszajn trees for any regular $k>\aleph_1$, we produce a model with many singular cardinals where both the singular cardinals hypothesis and weak square fail.
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  2.  6
    Polish Metric Spaces with Fixed Distance Set.Riccardo Camerlo, Alberto Marcone & Luca Motto Ros - 2020 - Annals of Pure and Applied Logic 171 (10):102832.
    We study Polish spaces for which a set of possible distances $A \subseteq R^+$ is fixed in advance. We determine, depending on the properties of A, the complexity of the collection of all Polish metric spaces with distances in A, obtaining also example of sets in some Wadge classes where not many natural examples are known. Moreover we describe the properties that A must have in order that all Polish spaces with distances in that set belong to a given class, (...)
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  3.  4
    Rules with Parameters in Modal Logic II.Emil Jeřábek - 2020 - Annals of Pure and Applied Logic 171 (10):102829.
  4.  3
    Modal Extension of Ideal Paraconsistent Four-Valued Logic and its Subsystem.Norihiro Kamide & Yoni Zohar - 2020 - Annals of Pure and Applied Logic 171 (10):102830.
    This study aims to introduce a modal extension M4CC of Arieli, Avron, and Zamansky's ideal paraconsistent four-valued logic 4CC as a Gentzen-type sequent calculus and prove the Kripke-completeness and cut-elimination theorems for M4CC. The logic M4CC is also shown to be decidable and embeddable into the normal modal logic S4. Furthermore, a subsystem of M4CC, which has some characteristic properties that do not hold for M4CC, is introduced and the Kripke-completeness and cut-elimination theorems for this subsystem are proved. This subsystem (...)
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  5.  5
    Algebraically Closed Structures in Positive Logic.Mohammed Belkasmi - 2020 - Annals of Pure and Applied Logic 171 (9):102822.
    In this paper we extend of the notion of algebraically closed given in the case of groups and skew fields to an arbitrary h-inductive theory. The main subject of this paper is the study of the notion of positive algebraic closedness and its relationship with the notion of positive closedness and the amalgamation property.
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  6.  5
    Perfect Tree Forcings for Singular Cardinals.Natasha Dobrinen, Dan Hathaway & Karel Prikry - 2020 - Annals of Pure and Applied Logic 171 (9):102827.
  7.  4
    Silver Type Theorems for Collapses.Moti Gitik - 2020 - Annals of Pure and Applied Logic 171 (9):102825.
    Let κ be a cardinal of cofinality \omega_1 witnessed by a club of cardinals (κ_\alpha | \alpha < \omega_1) . We study Silver's type effects of collapsing of κ^+_\alphas 's on κ^+ . A model in which κ^+_\alphas 's (and also κ^+) are collapsed on a stationary co-stationary set is constructed.
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  8.  4
    Epimorphism Surjectivity in Varieties of Heyting Algebras.T. Moraschini & J. J. Wannenburg - 2020 - Annals of Pure and Applied Logic 171 (9):102824.
    It was shown recently that epimorphisms need not be surjective in a variety K of Heyting algebras, but only one counter-example was exhibited in the literature until now. Here, a continuum of such examples is identified, viz. the variety generated by the Rieger-Nishimura lattice, and all of its (locally finite) subvarieties that contain the original counter-example K . It is known that, whenever a variety of Heyting algebras has finite depth, then it has surjective epimorphisms. In contrast, we show that (...)
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  9.  3
    A Premouse Inheriting Strong Cardinals From V.Farmer Schlutzenberg - 2020 - Annals of Pure and Applied Logic 171 (9):102826.
  10.  9
    The Theory of Ceers Computes True Arithmetic.Uri Andrews, Noah Schweber & Andrea Sorbi - 2020 - Annals of Pure and Applied Logic 171 (8):102811.
    We show that the theory of the partial order of computably enumerable equivalence relations (ceers) under computable reduction is 1-equivalent to true arithmetic. We show the same result for the structure comprised of the dark ceers and the structure comprised of the light ceers. We also show the same for the structure of L-degrees in the dark, light, or complete structure. In each case, we show that there is an interpretable copy of (N, +, \times) .
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  11.  3
    A Classification of the Cofinal Structures of Precompacta.Aviv Eshed, M. Vicenta Ferrer, Salvador Hernández, Piotr Szewczak & Boaz Tsaban - 2020 - Annals of Pure and Applied Logic 171 (8):102810.
    We provide a complete classification of the possible cofinal structures of the families of precompact (totally bounded) sets in general metric spaces, and compact sets in general complete metric spaces. Using this classification, we classify the cofinal structure of local bases in the groups C(X, R) of continuous real-valued functions on complete metric spaces X, with respect to the compact-open topology.
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  12.  2
    Some Constructions of Ultrafilters Over a Measurable Cardinal.Moti Gitik - 2020 - Annals of Pure and Applied Logic 171 (8):102821.
    Some non-normal κ-complete ultrafilters over a measurable κ with special properties are constructed. Questions by A. Kanamori [4] about infinite Rudin-Frolik sequences, discreteness and products are answered.
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  13.  5
    Computability of Pseudo-Cubes.Marko Horvat, Zvonko Iljazović & Bojan Pažek - 2020 - Annals of Pure and Applied Logic 171 (8):102823.
    We examine topological pairs (\Delta, \Sigma) which have computable type: if X is a computable topological space and f:\Delta \rightarrow X a topological embedding such that f(\Delta) and f(\Sigma) are semicomputable sets in X, then f(\Delta) is a computable set in X. It it known that (D, W) has computable type, where D is the Warsaw disc and W is the Warsaw circle. In this paper we identify a class of topological pairs which are similar to (D, W) and have (...)
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  14.  4
    A Forcing Axiom for a Non-Special Aronszajn Tree.John Krueger - 2020 - Annals of Pure and Applied Logic 171 (8):102820.
    Suppose that T^∗ is an ω_1-Aronszajn tree with no stationary antichain. We introduce a forcing axiom PFA(T^∗) for proper forcings which preserve these properties of T^∗. We prove that PFA(T^∗) implies many of the strong consequences of PFA, such as the failure of very weak club guessing, that all of the cardinal characteristics of the continuum are greater than ω_1, and the P-ideal dichotomy. On the other hand, PFA(T^∗) implies some of the consequences of diamond principles, such as the existence (...)
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  15.  2
    On Expansions Of.Quentin Lambotte & Françoise Point - 2020 - Annals of Pure and Applied Logic 171 (8):102809.
    Call a (strictly increasing) sequence (rn) of natural numbers regular if it satisfies the following condition: rn+1/rn→θ∈R>1∪{∞} and, if θ is algebraic, then (rn) satisfies a linear recurrence relation whose characteristic polynomial is the minimal polynomial of θ. Our main result states that (Z,+,0,R) is superstable whenever R is enumerated by a regular sequence. We give two proofs of this result. One relies on a result of E. Casanovas and M. Ziegler and the other on a quantifier elimination result. We (...)
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  16.  5
    Expander Construction in VNC1.Sam Buss, Valentine Kabanets, Antonina Kolokolova & Michal Koucký - 2020 - Annals of Pure and Applied Logic 171 (7):102796.
    We give a combinatorial analysis (using edge expansion) of a variant of the iterative expander construction due to Reingold, Vadhan, and Wigderson [44], and show that this analysis can be formalized in the bounded arithmetic system VNC^1 (corresponding to the “NC^1 reasoning”). As a corollary, we prove the assumption made by Jeřábek [28] that a construction of certain bipartite expander graphs can be formalized in VNC^1 . This in turn implies that every proof in Gentzen's sequent calculus LK of a (...)
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  17.  4
    Expansions of Real Closed Fields That Introduce No New Smooth Functions.Pantelis E. Eleftheriou & Alex Savatovsky - 2020 - Annals of Pure and Applied Logic 171 (7):102808.
  18.  5
    Turing Reducibility in the Fine Hierarchy.Alexander G. Melnikov, Victor L. Selivanov & Mars M. Yamaleev - 2020 - Annals of Pure and Applied Logic 171 (7):102766.
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  19.  6
    The Density Zero Ideal and the Splitting Number.Dilip Raghavan - 2020 - Annals of Pure and Applied Logic 171 (7):102807.
    The main result of this paper is an improvement of the upper bound on the cardinal invariant $cov^*(L_0)$ that was discovered in [11]. Here $L_0$ is the ideal of subsets of the set of natural numbers that have asymptotic density zero. This improved upper bound is also dualized to get a better lower bound on the cardinal $non^*(L_0)$. En route some variations on the splitting number are introduced and several relationships between these variants are proved.
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  20.  5
    M-Separable Spaces of Functions Are Productive in the Miller Model.Dušan Repovš & Lyubomyr Zdomskyy - 2020 - Annals of Pure and Applied Logic 171 (7):102806.
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  21.  9
    Herbrand's Theorem as Higher Order Recursion.Bahareh Afshari, Stefan Hetzl & Graham E. Leigh - 2020 - Annals of Pure and Applied Logic 171 (6):102792.
  22.  7
    Bilattice Logic of Epistemic Actions and Knowledge.Zeinab Bakhtiari, Hans van Ditmarsch & Umberto Rivieccio - 2020 - Annals of Pure and Applied Logic 171 (6):102790.
    Baltag, Moss, and Solecki proposed an expansion of classical modal logic, called logic of epistemic actions and knowledge (EAK), in which one can reason about knowledge and change of knowledge. Kurz and Palmigiano showed how duality theory provides a flexible framework for modeling such epistemic changes, allowing one to develop dynamic epistemic logics on a weaker propositional basis than classical logic (for example an intuitionistic basis). In this paper we show how the techniques of Kurz and Palmigiano can be further (...)
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  23.  6
    Characterizations of the Weakly Compact Ideal on Pλ.Brent Cody - 2020 - Annals of Pure and Applied Logic 171 (6):102791.
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  24.  3
    Some Lower Bounds on Shelah Rank in the Free Group.Javier de la Nuez González, Chloé Perin & Rizos Sklinos - 2020 - Annals of Pure and Applied Logic 171 (6):102794.
    We give some lower bounds on the Shelah rank of varieties in the free group whose coordinate groups are hyperbolic towers.
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  25.  6
    Embeddings Between Well-Orderings: Computability-Theoretic Reductions.Jun Le Goh - 2020 - Annals of Pure and Applied Logic 171 (6):102789.
    We study the computational content of various theorems with reverse mathematical strength around Arithmetical Transfinite Recursion (ATR_0) from the point of view of computability-theoretic reducibilities, in particular Weihrauch reducibility. Our main result states that it is equally hard to construct an embedding between two given well-orderings, as it is to construct a Turing jump hierarchy on a given well-ordering. This answers a question of Marcone. We obtain a similar result for Fraïssé's conjecture restricted to well-orderings.
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  26.  3
    Definable Groups in Models of Presburger Arithmetic.Alf Onshuus & Mariana Vicaría - 2020 - Annals of Pure and Applied Logic 171 (6):102795.
    This paper is devoted to understand groups definable in Presburger Arithmetic. We prove the following theorems: Theorem 1. Every group definable in a model of Presburger Arithmetic is abelian-by-finite. Theorem 2. Every bounded abelian group definable in a model of (Z, +, <) Presburger Arithmetic is definably isomorphic to (Z, +)^n mod out by a lattice.
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  27.  8
    Univalent polymorphism.Benno van den Berg - 2020 - Annals of Pure and Applied Logic 171 (6):102793.
    We show that Martin Hyland's effective topos can be exhibited as the homotopy category of a path category EFF. Path categories are categories of fibrant objects in the sense of Brown satisfying two additional properties and as such provide a context in which one can interpret many notions from homotopy theory and Homotopy Type Theory. Within the path category EFF one can identify a class of discrete fibrations which is closed under push forward along arbitrary fibrations (in other words, this (...)
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  28.  3
    Short Extenders Forcings – Doing Without Preparations.Moti Gitik - 2020 - Annals of Pure and Applied Logic 171 (5):102787.
    We introduce certain morass type structures and apply them to blowing up powers of singular cardinals. As a bonus, a forcing for adding clubs with finite conditions to higher cardinals is obtained.
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  29.  4
    Non-Finitely Axiomatisable Modal Product Logics with Infinite Canonical Axiomatisations.Christopher Hampson, Stanislav Kikot, Agi Kurucz & Sérgio Marcelino - 2020 - Annals of Pure and Applied Logic 171 (5):102786.
    Our concern is the axiomatisation problem for modal and algebraic logics that correspond to various fragments of two-variable first-order logic with counting quantifiers. In particular, we consider modal products with Diff, the propositional unimodal logic of the difference operator. We show that the two-dimensional product logic $Diff \times Diff$ is non-finitely axiomatisable, but can be axiomatised by infinitely many Sahlqvist axioms. We also show that its ‘square’ version (the modal counterpart of the substitution and equality free fragment of two-variable first-order (...)
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  30.  5
    Pincherle's Theorem in Reverse Mathematics and Computability Theory.Dag Normann & Sam Sanders - 2020 - Annals of Pure and Applied Logic 171 (5):102788.
    We study the logical and computational properties of basic theorems of uncountable mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a locally bounded function is bounded on certain domains, i.e. one of the first ‘local-to-global’ principles. It is well-known that such principles in analysis are intimately connected to (open-cover) compactness, but we nonetheless exhibit fundamental differences between compactness and Pincherle's theorem. For instance, the main question of Reverse Mathematics, namely which set existence axioms are necessary to (...)
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  31.  3
    The Tree Property at First and Double Successors of Singular Cardinals with an Arbitrary Gap.Alejandro Poveda - 2020 - Annals of Pure and Applied Logic 171 (5):102778.
  32.  5
    Ordered Asymptotic Classes of Finite Structures.Darío García - 2020 - Annals of Pure and Applied Logic 171 (4):102776.
    We introduce the concept of o-asymptotic classes of finite structures, melding ideas coming from 1-dimensional asymptotic classes and o-minimality. Along with several examples and non-examples of these classes, we present some classification theory results of their infinite ultraproducts: Every infinite ultraproduct of structures in an o-asymptotic class is superrosy of U^þ-rank 1, and NTP2 (in fact, inp-minimal).
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  33.  4
    On Subrecursive Complexity of Integration.Ivan Georgiev - 2020 - Annals of Pure and Applied Logic 171 (4):102777.
    We consider the complexity of the integration operator on real functions with respect to the subrecursive class M^2 . We prove that the definite integral of a uniformly M^2-computable analytic real function with M^2-computable limits is itself M^2-computable real number. We generalise this result to integrals with parameters and with varying limits. As an application, we show that the Euler-Mascheroni constant is M^2-computable.
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  34.  11
    Completeness Theorems for Σ–Additive Probabilistic Semantics.Nebojša Ikodinović, Zoran Ognjanović, Aleksandar Perović & Miodrag Rašković - 2020 - Annals of Pure and Applied Logic 171 (4):102755.
  35.  12
    Stationarily Ordered Types and the Number of Countable Models.Slavko Moconja & Predrag Tanović - 2020 - Annals of Pure and Applied Logic 171 (3):102765.
    We introduce the notions of stationarily ordered types and theories; the latter generalizes weak o-minimality and the former is a relaxed version of weak o-minimality localized at the locus of a single type. We show that forking, as a binary relation on elements realizing stationarily ordered types, is an equivalence relation and that each stationarily ordered type in a model determines some order-type as an invariant of the model. We study weak and forking non-orthogonality of stationarily ordered types, show that (...)
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  36.  7
    Elementary Inductive Dichotomy: Separation of Open and Clopen Determinacies with Infinite Alternatives.Kentaro Sato - 2020 - Annals of Pure and Applied Logic 171 (3):102754.
    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; (...)
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  37.  11
    Determinate Logic and the Axiom of Choice.J. P. Aguilera - 2020 - Annals of Pure and Applied Logic 171 (2):102745.
    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 (...)
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  38.  6
    Functional Representation of Finitely Generated Free Algebras in Subvarieties of BL-Algebras.Manuela Busaniche, José Luis Castiglioni & Noemí Lubomirsky - 2020 - Annals of Pure and Applied Logic 171 (2):102757.
    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.
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  39.  11
    Remarks on Generic Stability in Independent Theories.Gabriel Conant & Kyle Gannon - 2020 - Annals of Pure and Applied Logic 171 (2):102736.
    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 (...)
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  40.  5
    Uniformly Locally o-Minimal Structures and Locally o-Minimal Structures Admitting Local Definable Cell Decomposition.Masato Fujita - 2020 - Annals of Pure and Applied Logic 171 (2):102756.
    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 (...)
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  41.  9
    Feasibly Constructive Proofs of Succinct Weak Circuit Lower Bounds.Moritz Müller & Ján Pich - 2020 - Annals of Pure and Applied Logic 171 (2):102735.
  42.  7
    Resolution Over Linear Equations Modulo Two.Dmitry Itsykson & Dmitry Sokolov - 2020 - Annals of Pure and Applied Logic 171 (1):102722.
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  43.  8
    Algebraic Description of Limit Models in Classes of Abelian Groups.Marcos Mazari-Armida - 2020 - Annals of Pure and Applied Logic 171 (1):102723.
  44.  9
    Lyndon Interpolation Theorem of Instantial Neighborhood Logic – Constructively Via a Sequent Calculus.Junhua Yu - 2020 - Annals of Pure and Applied Logic 171 (1):102721.
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