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  1. Transitivity When the Same are Distinct.Eric de Araujo - 2022 - Erkenntnis 88 (7):2893-2909.
    It is widely assumed that the identity relation is, among other things, transitive. Some have proposed that the identity relation might hold between objects contingently or occasionally. If, on those proposals, identity is shown to not be transitive, then there is reason to reject such proposals. One such argument attempts to show that the identity relation on such proposals violates transitivity in cases of ‘simultaneous’ fissions and fusion. I argue that, even in those cases, contingent identity and occasional identity are (...)
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  2. A Correctness Proof for Al-Barakāt’s Logical Diagrams.Wilfrid Hodges - 2023 - Review of Symbolic Logic 16 (2):369-384.
    In Baghdad in the mid twelfth century Abū al-Barakāt proposes a radical new procedure for finding the conclusions of premise-pairs in syllogistic logic, and for identifying those premise-pairs that have no conclusions. The procedure makes no use of features of the standard Aristotelian apparatus, such as conversions or syllogistic figures. In place of these al-Barakāt writes out pages of diagrams consisting of labelled horizontal lines. He gives no instructions and no proof that the procedure will yield correct results. So the (...)
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  3. Rules and Self-Citation.Ori Simchen - 2023 - Journal for the History of Analytical Philosophy 11 (3):1-10.
    I discuss a neglected solution to the skeptical problem introduced by Lewis Carroll’s “What the Tortoise Said to Achilles” (1895) in terms of a self-citational inferential license. I then consider some responses to this solution. The most significant response on behalf of the skeptic utilizes the familiar distinction between two ways of accepting a rule: as action-guiding and as a mere truth. I argue that this is ultimately unsatisfactory and conclude by opting for an alternative conception of rules as representations (...)
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  4. Metafísica, lógica e outras coisas mais.Luiz Carlos Pereira, Marco A. Zingano & Lia Levy (eds.) - 2011 - Rio de Janeiro: Nau Editora.
    Livro em homenagem ao filósofo brasileiro Luiz Henrique Lopes, um dos maiores expoentes da filosofia analítica. Neste livro grandes nomes da filosofia brasileira discorrem sobre a filosofia analítica e vários assuntos da filosofia contemporânea.
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  5. Omnis Propositio Est Affirmativa; Ergo, Nulla Propositio Est Negativa (and the Paradox of Validity).Dahlquist Manuel - 2023 - In Theories of Paradox in the Middle Ages. LONDON: College Publication. pp. 100-129.
    In the first of the Insolubles in Chapter 8 of his Sophismata, Buridan contends that the inference Omnis propositio est affirmativa; ergo, nulla propositio est negativa (PS) is valid, even though it appeals to the self-reference in the conclusion to show that what we (following Read 2001) call the classical conception of validity (CCV) fails. This requires that we accept that there are good inferences in which a false conclusion follows from true premises. Partially following Hughes’ proposal (1982), we argue (...)
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  6. The Logic of Analogy.Avi Sion - 2023 - USA: Amazon/Kindle.
    The Logic of Analogy is a study of the valid logical forms of qualitative and quantitative analogical argument, and the rules pertaining to them. It investigates equally valid conflicting arguments, statistics-based arguments and their utility in science, arguments from precedent used in law-making or law-application, and examines subsumption in analogical terms. Included for purposes of illustration is a large section on Talmudic use of analogical reasoning.
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  7. Torn Between the Contours of Logic: Exploring Logical Normativity in Islamic Philosophical Theology.Abbas Ahsan & Marzuqa Karima - 2022 - European Journal of Analytic Philosophy 18 (2):(SI10)5-41.
    Western contemporary logic has been used to advance the field of Islamic philosophical theology, which historically utilised Aristotelian-Avicennian logic, on grounds of there being an inherent normativity in logic. This is in spite of the surrounding controversy on the status of logic in the Islamic theological tradition. The normative authority of logic means that it influences the content of what we ought to believe and how we ought to revise those beliefs. This paper seeks to demonstrate that, notwithstanding the incompatible (...)
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  8. On Stable Quotients.Krzysztof Krupiński & Adrián Portillo - 2022 - Notre Dame Journal of Formal Logic 63 (3):373-394.
    We solve two problems from a work of Haskel and Pillay concerning maximal stable quotients of groups ∧-definable in NIP theories. The first result says that if G is a ∧-definable group in a distal theory, then Gst=G00 (where Gst is the smallest ∧-definable subgroup with G∕Gst stable, and G00 is the smallest ∧-definable subgroup of bounded index). In order to get it, we prove that distality is preserved under passing from T to the hyperimaginary expansion Theq. The second result (...)
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  9. Introducing new work on indeterminacy and underdetermination.Mark Bowker - 2022 - Synthese 200 (6):1-14.
    This paper summarises the contributions to our Topical Collection on indeterminacy and underdetermination. The collection includes papers in ethics, metaethics, logic, metaphysics, epistemology, philosophy of science, philosophy of language and philosophy of computation.
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  10. The Dismissal of ‘Substance’ and ‘Being’ in Peirce’s Regenerated Logic.Maria Regina Brioschi - forthcoming - Logic and Logical Philosophy.
    After introducing the debate between substance philosophy and process philosophy, and clarifying the relevance of the category of ‘substance’ in Peirce’s thought, the present paper reconstructs the role of ‘substance’ and ‘being’ from Peirce’s early works to his theory of the proposition, provided after his studies on the logic of relatives. If those two categories apparently disappear in Peirce’s writings from the mid-1890s onwards, the account of ‘subject’ and ‘copula’ in Peirce’s analysis of the proposition allows one to grasp the (...)
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  11. Esbozo de una concepción particularista de las Leyes Lógicas.Miguel Agustín Álvarez Lisboa - 2021 - Culturas Cientificas 2 (1):04-22.
    El Anti-Excepcionalismo Lógico afirma que la Lógica es como cualquier otra ciencia. Si esta afirmación es cierta, entonces ella no sólo es revisable, sino que además todo lo que se puede decir sobre las ciencias aplica, mutatis mutandis, para la misma. El propósito de este artículo es explorar esta consecuencia del Anti-Excepcionalismo Lógico, acercando a la Filosofía de la Lógica el marco teórico de las Máquinas Nomológicas de Nancy Cartwright. De acuerdo con esta visión, lo que hay de verdadero en (...)
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  12. On intermediate inquisitive and dependence logics: An algebraic study.Davide Emilio Quadrellaro - 2022 - Annals of Pure and Applied Logic 173 (10):103143.
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  13. Formal Background for the Incompleteness and Undefinability Theorems.Richard Kimberly Heck - manuscript
    A teaching document I've used in my courses on truth and on incompleteness. Aimed at students who have a good grasp of basic logic, and decent math skills, it attempts to give them the background they need to understand a proper statement of the classic results due to Gödel and Tarski, and sketches their proofs. Topics covered include the notions of language and theory, the basics of formal syntax and arithmetization, formal arithmetic (Q and PA), representability, diagonalization, and the incompleteness (...)
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  14. History of Relating Logic. The Origin and Research Directions.Mateusz Klonowski - 2021 - Logic and Logical Philosophy 30 (4):579–629.
    In this paper, we present the history of and the research directions in relating logic. For this purpose we will describe Epstein's Programme, which postulates accounting for the content of sentences in logical research. We will focus on analysing the content relationship and Epstein's logics that are based on it, which are special cases of relating logic. Moreover, the set-assignment semantics will be discussed. Next, the Torunian Programme of Relating Semantics will be presented; this programme explores the various non-logical relationships (...)
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  15. Continuous sentences preserved under reduced products.Isaac Goldbring & H. Jerome Keisler - 2020 - Journal of Symbolic Logic:1-33.
    Answering a question of Cifú Lopes, we give a syntactic characterization of those continuous sentences that are preserved under reduced products of metric structures. In fact, we settle this question in the wider context of general structures as introduced by the second author.
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  16. Asymptotic analysis of skolem’s exponential functions.Alessandro Berarducci & Marcello Mamino - 2020 - Journal of Symbolic Logic:1-25.
    Skolem studied the germs at infinity of the smallest class of real valued functions on the positive real line containing the constant $1$, the identity function ${\mathbf {x}}$, and such that whenever f and g are in the set, $f+g,fg$ and $f^g$ are in the set. This set of germs is well ordered and Skolem conjectured that its order type is epsilon-zero. Van den Dries and Levitz computed the order type of the fragment below $2^{2^{\mathbf {x}}}$. Here we prove that (...)
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  17. The tree of tuples of a structure.Matthew Harrison-Trainor & Antonio Montalbán - 2022 - Journal of Symbolic Logic 87 (1):21-46.
    Our main result is that there exist structures which cannot be computably recovered from their tree of tuples. This implies that there are structures with no computable copies which nevertheless cannot code any information in a natural/functorial way.
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  18. Muchnik degrees and cardinal characteristics.Benoit Monin & André Nies - 2021 - Journal of Symbolic Logic 86 (2):471-498.
    A mass problem is a set of functions $\omega \to \omega $. For mass problems ${\mathcal {C}}, {\mathcal {D}}$, one says that ${\mathcal {C}}$ is Muchnik reducible to ${\mathcal {D}}$ if each function in ${\mathcal {C}}$ is computed by a function in ${\mathcal {D}}$. In this paper we study some highness properties of Turing oracles, which we view as mass problems. We compare them with respect to Muchnik reducibility and its uniform strengthening, Medvedev reducibility.For $p \in [0,1]$ let ${\mathcal {D}}$ (...)
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  19. The modal logic of set-theoretic potentialism and the potentialist maximality principles.Joel David Hamkins & Øystein Linnebo - 2022 - Review of Symbolic Logic 15 (1):1-35.
    We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and Löwe [14], including the use of buttons, switches, dials and ratchets. Among the potentialist conceptions we consider are: rank potentialism, Grothendieck–Zermelo potentialism, transitive-set potentialism, forcing potentialism, countable-transitive-model potentialism, countable-model potentialism, and others. In each case, we identify lower bounds for the modal validities, which are generally either S4.2 or S4.3, (...)
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  20. De Zolt’s Postulate: An Abstract Approach.Eduardo N. Giovannini, Edward H. Haeusler, Abel Lassalle-Casanave & Paulo A. S. Veloso - 2022 - Review of Symbolic Logic 15 (1):197-224.
    A theory of magnitudes involves criteria for their equivalence, comparison and addition. In this article we examine these aspects from an abstract viewpoint, by focusing on the so-called De Zolt’s postulate in the theory of equivalence of plane polygons (“If a polygon is divided into polygonal parts in any given way, then the union of all but one of these parts is not equivalent to the given polygon”). We formulate an abstract version of this postulate and derive it from some (...)
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  21. UFO: Unified Foundational Ontology.Giancarlo Guizzardi, Alessander Bottes Benevides, Claudemir M. Fonseca, João Paulo A. Almeida, Tiago Prince Sales & Daniele Porello - 2022 - Applied ontology 1 (17):167-210.
    The Unified Foundational Ontology (UFO) was developed over the last two decades by consistently putting together theories from areas such as formal ontology in philosophy, cognitive science, linguistics, and philosophical logics. It comprises a number of micro-theories addressing fundamental conceptual modeling notions, including entity types and relationship types. The aim of this paper is to summarize the current state of UFO, presenting a formalization of the ontology, along with the analysis of a number of cases to illustrate the application of (...)
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  22. Second Pisa Colloquium in Logic, Language and Epistemology.E. Moriconi & Laura Tesconi (eds.) - 2014 - ETS.
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  23. The Logica Yearbook 2012.Vit Puncochar & Petr Svarny (eds.) - 2013 - College Publications.
    This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2012, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.
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  24. Completeness and Doxastic Plurality for Topological Operators of Knowledge and Belief.Thomas Mormann - 2023 - Erkenntnis: 1 - 34, ONLINE.
    The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free topology) (...)
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  25. The Subject Matter of Logic: Explaining what logic is about.Elizabeth Olsen - 2021 - Dissertation, Victoria University of Wellington
    Logicians disagree about how validity—the very heart of logic—should be understood. Many different formal systems have been born due to this disagreement. This thesis examines how teachers explain the subject matter of logic to students in introductory logic textbooks, and demonstrates the different explanations teachers use. These differences help explain why logicians have different intuitions about validity.
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  26. Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs.Ivo Düntsch & Edwin Mares (eds.) - 2021 - Springer Verlag.
    This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart’s work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart. Alasdair Urquhart has made extremely important contributions to a (...)
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  27. Ω-Bibliography of Mathematical Logic: Classical Logic.Wolfgang Rautenberg (ed.) - 1987 - Berlin and Heidelberg: Springer.
    Gert H. Muller The growth of the number of publications in almost all scientific areas, as in the area of logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in their (...)
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  28. Formal Logic.Arthur Norman Prior - 1955 - Oxford, England: Oxford University Press.
    No further information has been provided for this title.
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  29. Pragmatic Logic.Kazimierz Ajdukiewicz - 1974 - Dordrecht and Boston: Reidel.
    When asked in 1962 on what he was working Kazimierz Ajdukiewicz replied: Several years ago Polish Scientific Publishers suggested that I pre pare a new edition of The Logical Foundations of Teaching, which I wrote 1 before 1939 as a contribution to The Encyclopaedia of Education. It was a small booklet covering elementary information about logical semantics and scientific methodology, information which in my opinion was necessary as a foundation of teaching and as an element of the education of any (...)
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  30. The Inextricable Link Between Conditionals and Logical Consequence.Matheus Silva - manuscript
    There is a profound, but frequently ignored relationship between logical consequence (formal implication) and material implication. The first repeats the patterns of the latter, but with a wider modal reach. It is argued that this kinship between formal and material implication simply means that they express the same kind of implication, but differ in scope. Formal implication is unrestricted material implication. This apparently innocuous observation has some significant corollaries: (1) conditionals are not connectives, but arguments; (2) the traditional examples of (...)
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  31. Iterability for (transfinite) stacks.Farmer Schlutzenberg - 2021 - Journal of Mathematical Logic 21 (2):2150008.
    We establish natural criteria under which normally iterable premice are iterable for stacks of normal trees. Let Ω be a regular uncountable cardinal. Let m < ω and M be an m-sound premouse and Σ be...
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  32. On wide Aronszajn trees in the presence of ma.Mirna Džamonja & Saharon Shelah - 2021 - Journal of Symbolic Logic 86 (1):210-223.
    A wide Aronszajn tree is a tree of size and height $\omega _{1}$ with no uncountable branches. We prove that under $MA$ there is no wide Aronszajn tree which is universal under weak embeddings. This solves an open question of Mekler and Väänänen from 1994. We also prove that under $MA$, every wide Aronszajn tree weakly embeds in an Aronszajn tree, which combined with a result of Todorčević from 2007, gives that under $MA$ every wide Aronszajn tree embeds into a (...)
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  33. on the epistemological significance of arguments from non transitive similarity.Friedrich Wilhelm Grafe - 2021 - Archive.Org.
    This paper aims to argue for, else illustrate the epistemological significance of the use of non transitive similarity relations, mapping only to "types", as methodologically being on a par with the use of transitive similarity relations (equivalence relations), mapping as well to "predicates". -/- In this paper the sketch of an exact but simple geometrical model of the above construct is followed by mentioning respective use cases for non transitive similarity relations from science and humanities. A well known metaphysics example (...)
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  34. Un alegato a favor del enfoque lógico en la teoría de la argumentación.Marc Jiménez-Rolland - 2020 - Quadripartita Ratio 10:21-35.
    El estudio actual de la argumentación se encuentra distanciado de la lógica. En este artículo sostengo que restaurar el vínculo del estudio de la argumentación con esta disciplina podría resultar benéfico para la metas descriptivas y normativas de este campo de investigación. Tras destacar algunos aspectos del surgimiento la teoría de la argumentación contemporánea, enfatizando la idea de "perspectivas", explico cómo el reconocimiento de sus objetivos y tareas volvió problemática la coexistencia de varios enfoques o aproximaciones para el estudio de (...)
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  35. Towards World Identification in Description Logics.Farshad Badie - forthcoming - Logical Investigations:115–134.
    Logical analysis of the applicability of nominals (which are introduced by hybrid logic) in the formal descriptions of the world (within modern knowledge representation and semantics-based systems) is very important because nominals, as second sorts of propositional symbols, can support logical identification of the described world at specific [temporal and/or spacial] states. This paper will focus on answering the philosophical-logical question of ‘how a fundamental world description in description logic (DL) and a nominal can be related to each other?’. Based (...)
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  36. Anti-essentialism, modal relativity, and alternative material-origin counterfactuals.Frederique Janssen-Lauret - 2021 - Synthese 199 (3-4):8379-8398.
    In ordinary language, in the medical sciences, and in the overlap between them, we frequently make claims which imply that we might have had different gametic origins from the ones we actually have. Such statements seem intuitively true and coherent. But they counterfactually ascribe different DNA to their referents and therefore contradict material-origin essentialism, which Kripke and his followers argue is intuitively obvious. In this paper I argue, using examples from ordinary language and from philosophy of medicine and bioethics, that (...)
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  37. Gödel diffeomorphisms.Matthew Foreman - 2020 - Bulletin of Symbolic Logic 26 (3-4):219-223.
    In 1932, von Neumann proposed classifying the statistical behavior of differentiable systems. Joint work of B. Weiss and the author proved that the classification problem is complete analytic. Based on techniques in that proof, one is able to show that the collection of recursive diffeomorphisms of the 2-torus that are isomorphic to their inverses is $\Pi ^0_1$-hard via a computable 1-1 reduction. As a corollary there is a diffeomorphism that is isomorphic to its inverse if and only if the Riemann (...)
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  38. Structural fixed-point theorems.Brian Rabern & Landon Rabern - manuscript
    The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality -- these are the so-called "dangerous" directed graphs. Building on Rabern, et. al (2013) we reformulate this problem in terms of fixed points of certain functions, thereby boiling it down to get (...)
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  39. The fundamental theorem of central element theory.Mariana Vanesa Badano & Diego Jose Vaggione - 2020 - Journal of Symbolic Logic 85 (4):1599-1606.
    We give a short proof of the fundamental theorem of central element theory. The original proof is constructive and very involved and relies strongly on the fact that the class be a variety. Here we give a more direct nonconstructive proof which applies for the more general case of a first-order class which is both closed under the formation of direct products and direct factors.
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  40. A metric version of schlichting’s theorem.Itaï Ben Yaacov & Frank O. Wagner - 2020 - Journal of Symbolic Logic 85 (4):1607-1613.
    If ${\mathfrak {F}}$ is a type-definable family of commensurable subsets, subgroups or subvector spaces in a metric structure, then there is an invariant subset, subgroup or subvector space commensurable with ${\mathfrak {F}}$. This in particular applies to type-definable or hyper-definable objects in a classical first-order structure.
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  41. Dimension inequality for a definably complete uniformly locally o-minimal structure of the second kind.Masato Fujita - 2020 - Journal of Symbolic Logic 85 (4):1654-1663.
    Consider a definably complete uniformly locally o-minimal expansion of the second kind of a densely linearly ordered abelian group. Let $f:X \rightarrow R^n$ be a definable map, where X is a definable set and R is the universe of the structure. We demonstrate the inequality $\dim ) \leq \dim $ in this paper. As a corollary, we get that the set of the points at which f is discontinuous is of dimension smaller than $\dim $. We also show that the (...)
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  42. Multidimensional exact classes, smooth approximation and bounded 4-types.Daniel Wolf - 2020 - Journal of Symbolic Logic 85 (4):1305-1341.
    In connection with the work of Anscombe, Macpherson, Steinhorn and the present author in [1] we investigate the notion of a multidimensional exact class, a special kind of multidimensional asymptotic class with measuring functions that yield the exact sizes of definable sets, not just approximations. We use results about smooth approximation [24] and Lie coordinatization [13] to prove the following result, as conjectured by Macpherson: For any countable language $\mathcal {L}$ and any positive integer d the class $\mathcal {C}$ of (...)
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  43. Думата, нейното значение и нейната близост.Vasil Penchev - 1995 - Philosophical Alternatives 4 (6):105-113.
    Предложен е семантичен подход към логиката, в рамките на какъвто е вид дискурс, отличим със своята тавтологичност. На тази основа е даден пример и сравнение с психоаналитичен (Фройдистки) дискурс.
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  44. Homogeneous structures with nonuniversal automorphism groups.Wiesław Kubiś & Saharon Shelah - 2020 - Journal of Symbolic Logic 85 (2):817-827.
    We present three examples of countable homogeneous structures whose automorphism groups are not universal, namely, fail to contain isomorphic copies of all automorphism groups of their substructures.Our first example is a particular case of a rather general construction on Fraïssé classes, which we call diversification, leading to automorphism groups containing copies of all finite groups. Our second example is a special case of another general construction on Fraïssé classes, the mixed sums, leading to a Fraïssé class with all finite symmetric (...)
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  45. The Ketonen order.Gabriel Goldberg - 2020 - Journal of Symbolic Logic 85 (2):585-604.
    We study a partial order on countably complete ultrafilters introduced by Ketonen [2] as a generalization of the Mitchell order. The following are our main results: the order is wellfounded; its linearity is equivalent to the Ultrapower Axiom, a principle introduced in the author’s dissertation [1]; finally, assuming the Ultrapower Axiom, the Ketonen order coincides with Lipschitz reducibility in the sense of generalized descriptive set theory.
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  46. Coding in graphs and linear orderings.Julia F. Knight, Alexandra A. Soskova & Stefan V. Vatev - 2020 - Journal of Symbolic Logic 85 (2):673-690.
    There is a Turing computable embedding $\Phi $ of directed graphs $\mathcal {A}$ in undirected graphs. Moreover, there is a fixed tuple of formulas that give a uniform effective interpretation; i.e., for all directed graphs $\mathcal {A}$, these formulas interpret $\mathcal {A}$ in $\Phi $. It follows that $\mathcal {A}$ is Medvedev reducible to $\Phi $ uniformly; i.e., $\mathcal {A}\leq _s\Phi $ with a fixed Turing operator that serves for all $\mathcal {A}$. We observe that there is a graph G (...)
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  47. Deciding some Maltsev conditions in finite idempotent algebras.Alexandr Kazda & Matt Valeriote - 2020 - Journal of Symbolic Logic 85 (2):539-562.
    In this paper we investigate the computational complexity of deciding if the variety generated by a given finite idempotent algebra satisfies a special type of Maltsev condition that can be specified using a certain kind of finite labelled path. This class of Maltsev conditions includes several well known conditions, such as congruence permutability and having a sequence of n Jónsson terms, for some given n. We show that for such “path defined” Maltsev conditions, the decision problem is polynomial-time solvable.
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  48. The complexity of homeomorphism relations on some classes of compacta.Paweł Krupski & Benjamin Vejnar - 2020 - Journal of Symbolic Logic 85 (2):733-748.
    We prove that the homeomorphism relation between compact spaces can be continuously reduced to the homeomorphism equivalence relation between absolute retracts, which strengthens and simplifies recent results of Chang and Gao, and Cieśla. It follows then that the homeomorphism relation of absolute retracts is Borel bireducible with the universal orbit equivalence relation. We also prove that the homeomorphism relation between regular continua is classifiable by countable structures and hence it is Borel bireducible with the universal orbit equivalence relation of the (...)
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  49. A descriptive Main Gap Theorem.Francesco Mangraviti & Luca Motto Ros - 2020 - Journal of Mathematical Logic 21 (1):2050025.
    Answering one of the main questions of [S.-D. Friedman, T. Hyttinen and V. Kulikov, Generalized descriptive set theory and classification theory, Mem. Amer. Math. Soc. 230 80, Chap. 7], we show that there is a tight connection between the depth of a classifiable shallow theory [Formula: see text] and the Borel rank of the isomorphism relation [Formula: see text] on its models of size [Formula: see text], for [Formula: see text] any cardinal satisfying [Formula: see text]. This is achieved by (...)
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  50. Pseudofinite difference fields and counting dimensions.Tingxiang Zou - 2020 - Journal of Mathematical Logic 21 (1):2050022.
    We study a family of ultraproducts of finite fields with the Frobenius automorphism in this paper. Their theories have the strict order property and TP2. But the coarse pseudofinite dimension of the definable sets is definable and integer-valued. Moreover, we also discuss the possible connection between coarse dimension and transformal transcendence degree in these difference fields.
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