Year:

  1.  2
    Generalised stability of ultraproducts of finite residue rings.Ricardo Isaac Bello Aguirre - 2021 - Archive for Mathematical Logic 60 (7):815-829.
    We study ultraproducts of finite residue rings \ where \ is a non-principal ultrafilter. We find sufficient conditions of the ultrafilter \ to determine if the resulting ultraproduct \ has simple, NIP, \ but not simple nor NIP, or \ theory, noting that all these four cases occur.
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  2.  1
    Definable connectedness of randomizations of groups.Alexander Berenstein & Jorge Daniel Muñoz - 2021 - Archive for Mathematical Logic 60 (7):1019-1041.
    We study randomizations of definable groups. Whenever the underlying theory is stable or NIP and the group is definably amenable, we show its randomization is definably connected.
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  3.  2
    Factorizing the $$\mathbf {Top}$$ Top – $$\mathbf {Loc}$$ Loc adjunction through positive topologies.Francesco Ciraulo, Tatsuji Kawai & Samuele Maschio - 2021 - Archive for Mathematical Logic 60 (7):967-979.
    We characterize the category of Sambin’s positive topologies as the result of the Grothendieck construction applied to a doctrine over the category Loc of locales. We then construct an adjunction between the category of positive topologies and that of topological spaces Top, and show that the well-known adjunction between Top and Loc factors through the constructed adjunction.
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  4.  7
    The abstract type of the real numbers.Fernando Ferreira - 2021 - Archive for Mathematical Logic 60 (7):1005-1017.
    In finite type arithmetic, the real numbers are represented by rapidly converging Cauchy sequences of rational numbers. Ulrich Kohlenbach introduced abstract types for certain structures such as metric spaces, normed spaces, Hilbert spaces, etc. With these types, the elements of the spaces are given directly, not through the mediation of a representation. However, these abstract spaces presuppose the real numbers. In this paper, we show how to set up an abstract type for the real numbers. The appropriateness of our construction (...)
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  5.  4
    The automorphism group and definability of the jump operator in the $$\omega $$ ω -enumeration degrees.Hristo Ganchev & Andrey C. Sariev - 2021 - Archive for Mathematical Logic 60 (7):909-925.
    In the present paper, we show the first-order definability of the jump operator in the upper semi-lattice of the \-enumeration degrees. As a consequence, we derive the isomorphicity of the automorphism groups of the enumeration and the \-enumeration degrees.
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  6.  8
    The theories of Baldwin–Shi hypergraphs and their atomic models.Danul K. Gunatilleka - 2021 - Archive for Mathematical Logic 60 (7):879-908.
    We show that the quantifier elimination result for the Shelah-Spencer almost sure theories of sparse random graphs \\) given by Laskowski extends to their various analogues. The analogues will be obtained as theories of generic structures of certain classes of finite structures with a notion of strong substructure induced by rank functions and we will call the generics Baldwin–Shi hypergraphs. In the process we give a method of constructing extensions whose ‘relative rank’ is negative but arbitrarily small in context. We (...)
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  7.  2
    Short note: Least fixed points versus least closed points.Gerhard Jäger - 2021 - Archive for Mathematical Logic 60 (7):831-835.
    This short note is on the question whether the intersection of all fixed points of a positive arithmetic operator and the intersection of all its closed points can proved to be equivalent in a weak fragment of second order arithmetic.
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  8.  7
    Proof-theoretic uniform boundedness and bounded collection principles and countable Heine–Borel compactness.Ulrich Kohlenbach - 2021 - Archive for Mathematical Logic 60 (7):995-1003.
    In this note we show that proof-theoretic uniform boundedness or bounded collection principles which allow one to formalize certain instances of countable Heine–Borel compactness in proofs using abstract metric structures must be carefully distinguished from an unrestricted use of countable Heine–Borel compactness.
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  9.  5
    Pointwise complexity of the derivative of a computable function.Ethan McCarthy - 2021 - Archive for Mathematical Logic 60 (7):981-994.
    We explore the relationship between analytic behavior of a computable real valued function and the computability-theoretic complexity of the individual values of its derivative almost-everywhere. Given a computable function f, the values of its derivative \\), where they are defined, are uniformly computable from \, the Turing jump of the input. It is known that when f is \, the values of \\) are actually computable from x. We construct a \ function f so that, almost everywhere, \\ge _T x'\). (...)
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  10.  5
    Monotonic modal logics with a conjunction.Paula Menchón & Sergio Celani - 2021 - Archive for Mathematical Logic 60 (7):857-877.
    Monotone modal logics have emerged in several application areas such as computer science and social choice theory. Since many of the most studied selfextensional logics have a conjunction, in this paper we study some distributive extensions obtained from a semilattice based deductive system with monotonic modal operators, and we give them neighborhood and algebraic semantics. For each logic defined our main objective is to prove completeness with respect to its characteristic class of monotonic frames.
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  11.  2
    On the spectra of cardinalities of branches of Kurepa trees.Márk Poór - 2021 - Archive for Mathematical Logic 60 (7):927-966.
    We are interested in the possible sets of cardinalities of branches of Kurepa trees in models of ZFC \ CH. In this paper we present a sufficient condition to be consistently the set of cardinalities of branches of Kurepa trees.
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  12.  3
    Hereditary G-compactness.Tomasz Rzepecki - 2021 - Archive for Mathematical Logic 60 (7):837-856.
    We introduce the notion of hereditary G-compactness. We provide a sufficient condition for a poset to not be hereditarily G-compact, which we use to show that any linear order is not hereditarily G-compact. Assuming that a long-standing conjecture about unstable NIP theories holds, this implies that an NIP theory is hereditarily G-compact if and only if it is stable -categorical theories). We show that if G is definable over A in a hereditarily G-compact theory, then \. We also include a (...)
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  13.  7
    Proof theory for heterogeneous logic combining formulas and diagrams: proof normalization.Ryo Takemura - 2021 - Archive for Mathematical Logic 60 (7):783-813.
    We extend natural deduction for first-order logic by introducing diagrams as components of formal proofs. From the viewpoint of FOL, we regard a diagram as a deductively closed conjunction of certain FOL formulas. On the basis of this observation, we first investigate basic heterogeneous logic wherein heterogeneous inference rules are defined in the styles of conjunction introduction and elimination rules of FOL. By examining what is a detour in our heterogeneous proofs, we discuss that an elimination-introduction pair of rules constitutes (...)
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  14.  6
    Infinite Decreasing Chains in the Mitchell Order.Omer Ben-Neria & Sandra Müller - 2021 - Archive for Mathematical Logic 60 (6):771-781.
    It is known that the behavior of the Mitchell order substantially changes at the level of rank-to-rank extenders, as it ceases to be well-founded. While the possible partial order structure of the Mitchell order below rank-to-rank extenders is considered to be well understood, little is known about the structure in the ill-founded case. The purpose of the paper is to make a first step in understanding this case, by studying the extent to which the Mitchell order can be ill-founded. Our (...)
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  15.  4
    Model Completeness and Relative Decidability.Jennifer Chubb, Russell Miller & Reed Solomon - 2021 - Archive for Mathematical Logic 60 (6):721-735.
    We study the implications of model completeness of a theory for the effectiveness of presentations of models of that theory. It is immediate that for a computable model A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {A}$$\end{document} of a computably enumerable, model complete theory, the entire elementary diagram E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document} must be decidable. We prove that indeed a c.e. theory T is model complete if and only if there is a (...)
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  16. Interpreting the compositional truth predicate in models of arithmetic.Cezary Cieśliński - 2021 - Archive for Mathematical Logic 60 (6):749-770.
    We present a construction of a truth class (an interpretation of a compositional truth predicate) in an arbitrary countable recursively saturated model of first-order arithmetic. The construction is fully classical in that it employs nothing more than the classical techniques of formal proof theory.
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  17.  3
    Towers and clubs.Pierre Matet - 2021 - Archive for Mathematical Logic 60 (6):683-719.
    We revisit several results concerning club principles and nonsaturation of the nonstationary ideal, attempting to improve them in various ways. So we typically deal with a ideal J extending the nonstationary ideal on a regular uncountable cardinal \, our goal being to witness the nonsaturation of J by the existence of towers ).
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  18.  10
    Forcing the Mapping Reflection Principle by Finite Approximations.Tadatoshi Miyamoto & Teruyuki Yorioka - 2021 - Archive for Mathematical Logic 60 (6):737-748.
    Moore introduced the Mapping Reflection Principle and proved that the Bounded Proper Forcing Axiom implies that the size of the continuum is ℵ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\aleph _2$$\end{document}. The Mapping Reflection Principle follows from the Proper Forcing Axiom. To show this, Moore utilized forcing notions whose conditions are countable objects. Chodounský–Zapletal introduced the Y-Proper Forcing Axiom that is a weak fragments of the Proper Forcing Axiom but implies some important conclusions from the Proper Forcing Axiom, (...)
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  19.  2
    Independence-friendly logic without Henkin quantification.Fausto Barbero, Lauri Hella & Raine Rönnholm - 2021 - Archive for Mathematical Logic 60 (5):547-597.
    We analyze the expressive resources of \ logic that do not stem from Henkin quantification. When one restricts attention to regular \ sentences, this amounts to the study of the fragment of \ logic which is individuated by the game-theoretical property of action recall. We prove that the fragment of prenex AR sentences can express all existential second-order properties. We then show that the same can be achieved in the non-prenex fragment of AR, by using “signalling by disjunction” instead of (...)
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  20.  7
    Formalism and Hilbert’s understanding of consistency problems.Michael Detlefsen - 2021 - Archive for Mathematical Logic 60 (5):529-546.
    Formalism in the philosophy of mathematics has taken a variety of forms and has been advocated for widely divergent reasons. In Sects. 1 and 2, I briefly introduce the major formalist doctrines of the late nineteenth and early twentieth centuries. These are what I call empirico-semantic formalism, game formalism and instrumental formalism. After describing these views, I note some basic points of similarity and difference between them. In the remainder of the paper, I turn my attention to Hilbert’s instrumental formalism. (...)
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  21.  3
    24th Workshop on Logic, Language, Information and Computation—WoLLIC 2017.Juliette Kennedy & Ruy de Queiroz - 2021 - Archive for Mathematical Logic 60 (5):525-527.
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  22.  4
    On ultrafilter extensions of first-order models and ultrafilter interpretations.Nikolai L. Poliakov & Denis I. Saveliev - 2021 - Archive for Mathematical Logic 60 (5):625-681.
    There exist two known types of ultrafilter extensions of first-order models, both in a certain sense canonical. One of them comes from modal logic and universal algebra, and in fact goes back to Jónsson and Tarski :891–939, 1951; 74:127–162, 1952). Another one The infinity project proceeding, Barcelona, 2012) comes from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups as its main precursor. By a classical fact of general topology, the space of ultrafilters over a discrete space is (...)
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  23.  6
    Knowledge, behavior, and rationality: rationalizability in epistemic games.Todd Stambaugh & Rohit Parikh - 2021 - Archive for Mathematical Logic 60 (5):599-623.
    In strategic situations, agents base actions on knowledge and beliefs. This includes knowledge about others’ strategies and preferences over strategy profiles, but also about other external factors. Bernheim and Pearce in 1984 independently defined the game theoretic solution concept of rationalizability, which is built on the premise that rational agents will only take actions that are the best response to some situation that they consider possible. This accounts for other agents’ rationality as well, limiting the strategies to which a particular (...)
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  24.  8
    Tree-like constructions in topology and modal logic.G. Bezhanishvili, N. Bezhanishvili, J. Lucero-Bryan & J. Van Mill - 2021 - Archive for Mathematical Logic 60 (3):265-299.
    Within ZFC, we develop a general technique to topologize trees that provides a uniform approach to topological completeness results in modal logic with respect to zero-dimensional Hausdorff spaces. Embeddings of these spaces into well-known extremally disconnected spaces then gives new completeness results for logics extending S4.2.
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  25.  6
    Small sets in Mann pairs.Pantelis E. Eleftheriou - 2021 - Archive for Mathematical Logic 60 (3):317-327.
    Let \ be an expansion of a real closed field \ by a dense subgroup G of \ with the Mann property. We prove that the induced structure on G by \ eliminates imaginaries. As a consequence, every small set X definable in \ can be definably embedded into some \, uniformly in parameters. These results are proved in a more general setting, where \ is an expansion of an o-minimal structure \ by a dense set \, satisfying three tameness (...)
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  26.  7
    Quantum logic is undecidable.Tobias Fritz - 2021 - Archive for Mathematical Logic 60 (3):329-341.
    We investigate the first-order theory of closed subspaces of complex Hilbert spaces in the signature \\), where ‘\’ is the orthogonality relation. Our main result is that already its quasi-identities are undecidable: there is no algorithm to decide whether an implication between equations and orthogonality relations implies another equation. This is a corollary of a recent result of Slofstra in combinatorial group theory. It follows upon reinterpreting that result in terms of the hypergraph approach to quantum contextuality, for which it (...)
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  27.  10
    Strong downward Löwenheim–Skolem theorems for stationary logics, II: reflection down to the continuum.Sakaé Fuchino, André Ottenbreit Maschio Rodrigues & Hiroshi Sakai - 2021 - Archive for Mathematical Logic 60 (3):495-523.
    Continuing, we study the Strong Downward Löwenheim–Skolem Theorems of the stationary logic and their variations. In Fuchino et al. it has been shown that the SDLS for the ordinary stationary logic with weak second-order parameters \. This SDLS is shown to be equivalent to an internal version of the Diagonal Reflection Principle down to an internally stationary set of size \. We also consider a version of the stationary logic and show that the SDLS for this logic in internal interpretation (...)
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  28.  7
    Another method for constructing models of not approachability and not SCH.Moti Gitik - 2021 - Archive for Mathematical Logic 60 (3):469-475.
    We present a new method of constructing a model of \SCH+\AP.
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  29.  13
    Cichoń’s diagram and localisation cardinals.Martin Goldstern & Lukas Daniel Klausner - 2021 - Archive for Mathematical Logic 60 (3):343-411.
    We reimplement the creature forcing construction used by Fischer et al. :1045–1103, 2017. https://doi.org/10.1007/S00153-017-0553-8. arXiv:1402.0367 [math.LO]) to separate Cichoń’s diagram into five cardinals as a countable support product. Using the fact that it is of countable support, we augment our construction by adding uncountably many additional cardinal characteristics, sometimes referred to as localisation cardinals.
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  30.  5
    Sofic Profiles of $$S(\omega )$$ and Computability.Aleksander Ivanov - 2021 - Archive for Mathematical Logic 60 (3-4):477-494.
    We show that for every sofic chunk E there is a bijective homomorphism \, where \ is a chunk of the group of computable permutations of \ so that the approximating morphisms of E can be viewed as restrictions of permutations of \ to finite subsets of \. Using this we study some relevant effectivity conditions associated with sofic chunks and their profiles.
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  31.  9
    Keisler’s order via Boolean ultrapowers.Francesco Parente - 2021 - Archive for Mathematical Logic 60 (3):425-439.
    In this paper, we provide a new characterization of Keisler’s order in terms of saturation of Boolean ultrapowers. To do so, we apply and expand the framework of ‘separation of variables’ recently developed by Malliaris and Shelah. We also show that good ultrafilters on Boolean algebras are precisely the ones which capture the maximum class in Keisler’s order, answering a question posed by Benda in 1974.
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  32.  3
    Axiomatic theory of betweenness.Sanaz Azimipour & Pavel Naumov - 2021 - Archive for Mathematical Logic 60 (1):227-239.
    Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three sets of points. The main technical result is a sound and complete logical system describing universal properties of this relation between sets of vertices of a graph.
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  33.  5
    Selection Properties of the Split Interval and the Continuum Hypothesis.Taras Banakh - 2021 - Archive for Mathematical Logic 60 (1-2):121-133.
    We prove that every usco multimap $$\varPhi :X\rightarrow Y$$ Φ : X → Y from a metrizable separable space X to a GO-space Y has an $$F_\sigma $$ F σ -measurable selection. On the other hand, for the split interval $${\ddot{\mathbb I}}$$ I ¨ and the projection $$P:{{\ddot{\mathbb I}}}^2\rightarrow \mathbb I^2$$ P : I ¨ 2 → I 2 of its square onto the unit square $$\mathbb I^2$$ I 2, the usco multimap $${P^{-1}:\mathbb I^2\multimap {{\ddot{\mathbb I}}}^2}$$ P - 1 : (...)
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  34.  4
    Some Complete $$\omega $$-Powers of a One-Counter Language, for Any Borel Class of Finite Rank.Olivier Finkel & Dominique Lecomte - 2021 - Archive for Mathematical Logic 60 (1-2):161-187.
    We prove that, for any natural number \, we can find a finite alphabet \ and a finitary language L over \ accepted by a one-counter automaton, such that the \-power $$\begin{aligned} L^\infty :=\{ w_0w_1\ldots \in \Sigma ^\omega \mid \forall i\in \omega ~~w_i\in L\} \end{aligned}$$is \-complete. We prove a similar result for the class \.
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  35.  5
    Strong Downward Löwenheim–Skolem Theorems for Stationary Logics, I.Sakaé Fuchino, André Ottenbreit Maschio Rodrigues & Hiroshi Sakai - 2021 - Archive for Mathematical Logic 60 (1-2):17-47.
    This note concerns the model theoretic properties of logics extending the first-order logic with monadic second-order variables equipped with the stationarity quantifier. The eight variations of the strong downward Löwenheim–Skolem Theorem down to <ℵ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<\aleph _2$$\end{document} for this logic with the interpretation of second-order variables as countable subsets of the structures are classified into four principles. The strongest of these four is shown to be equivalent to the conjunction of CH and the (...)
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  36.  5
    Characterising Brouwer’s continuity by bar recursion on moduli of continuity.Makoto Fujiwara & Tatsuji Kawai - 2021 - Archive for Mathematical Logic 60 (1):241-263.
    We identify bar recursion on moduli of continuity as a fundamental notion of constructive mathematics. We show that continuous functions from the Baire space \ to the natural numbers \ which have moduli of continuity with bar recursors are exactly those functions induced by Brouwer operations. The connection between Brouwer operations and bar induction allows us to formulate several continuity principles on the Baire space stated in terms of bar recursion on continuous moduli which naturally characterise some variants of bar (...)
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  37.  6
    On countably saturated linear orders and certain class of countably saturated graphs.Ziemowit Kostana - 2021 - Archive for Mathematical Logic 60 (1):189-209.
    The idea of this paper is to explore the existence of canonical countably saturated models for different classes of structures. It is well-known that, under CH, there exists a unique countably saturated linear order of cardinality \. We provide some examples of pairwise non-isomorphic countably saturated linear orders of cardinality \, under different set-theoretic assumptions. We give a new proof of the old theorem of Harzheim, that the class of countably saturated linear orders has a uniquely determined one-element basis. From (...)
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  38.  3
    First-order concatenation theory with bounded quantifiers.Lars Kristiansen & Juvenal Murwanashyaka - 2021 - Archive for Mathematical Logic 60 (1):77-104.
    We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.
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  39.  6
    Some Complete Ω\documentclass[12pt]{Minimal} \usepackage{Amsmath} \usepackage{Wasysym} \usepackage{Amsfonts} \usepackage{Amssymb} \usepackage{Amsbsy} \usepackage{Mathrsfs} \usepackage{Upgreek} \setlength{\oddsidemargin}{-69pt} \begin{Document}$$\omega $$\end{Document}-Powers of a One-Counter Language, for Any Borel Class of Finite Rank. [REVIEW]Dominique Lecomte & Olivier Finkel - 2021 - Archive for Mathematical Logic 60 (1-2):161-187.
    We prove that, for any natural number n≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 1$$\end{document}, we can find a finite alphabet Σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma $$\end{document} and a finitary language L over Σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma $$\end{document} accepted by a one-counter automaton, such that the ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-power L∞:={w0w1…∈Σω∣∀i∈ωwi∈L}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} (...)
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  40.  1
    Continuous Logic and Embeddings of Lebesgue Spaces.Timothy H. McNicholl - 2021 - Archive for Mathematical Logic 60 (1-2):105-119.
    We use the compactness theorem of continuous logic to give a new proof that Lr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^r$$\end{document} isometrically embeds into Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document} whenever 1≤p≤r≤2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1 \le p \le r \le 2$$\end{document}. We will also give a proof for the complex case. This will involve a new characterization of complex Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} (...)
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  41.  2
    A note on uniform density in weak arithmetical theories.Duccio Pianigiani & Andrea Sorbi - 2021 - Archive for Mathematical Logic 60 (1):211-225.
    Answering a question raised by Shavrukov and Visser :569–582, 2014), we show that the lattice of \-sentences ) over any computable enumerable consistent extension T of \ is uniformly dense. We also show that for every \ and \ refer to the known hierarchies of arithmetical formulas introduced by Burr for intuitionistic arithmetic) the lattices of \-sentences over any c.e. consistent extension T of the intuitionistic version of Robinson Arithmetic \ are uniformly dense. As an immediate consequence of the proof, (...)
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  42.  2
    $$AD_{Mathbb {R}}$$ A D R Implies That All Sets of Reals Are $$Theta $$ Θ Universally Baire. [REVIEW]Grigor Sargsyan - 2021 - Archive for Mathematical Logic 60 (1-2):1-15.
    We show that assuming the determinacy of all games on reals, every set of reals is Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta $$\end{document} universally baire.
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  43.  11
    $$AD_{Mathbb {R}}$$ A D R Implies That All Sets of Reals Are $$Theta $$ Θ Universally Baire.Grigor Sargsyan - 2021 - Archive for Mathematical Logic 60 (1-2):1-15.
    We show that assuming the determinacy of all games on reals, every set of reals is \ universally baire.
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  44.  6
    Strong cell decomposition property in o-minimal traces.Somayyeh Tari - 2021 - Archive for Mathematical Logic 60 (1):135-144.
    Strong cell decomposition property has been proved in non-valuational weakly o-minimal expansions of ordered groups. In this note, we show that all o-minimal traces have strong cell decomposition property. Also after introducing the notion of irrational nonvaluational cut in arbitrary o-minimal structures, we show that every expansion of o-minimal structures by irrational nonvaluational cuts is an o-minimal trace.
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    Ring Structure Theorems and Arithmetic Comprehension.Huishan Wu - 2021 - Archive for Mathematical Logic 60 (1-2):145-160.
    Schur’s Lemma says that the endomorphism ring of a simple left R-module is a division ring. It plays a fundamental role to prove classical ring structure theorems like the Jacobson Density Theorem and the Wedderburn–Artin Theorem. We first define the endomorphism ring of simple left R-modules by their Π10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^{0}_{1}$$\end{document} subsets and show that Schur’s Lemma is provable in RCA0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm RCA_{0}$$\end{document}. A ring (...)
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