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  1. Peter Schroeder-Heister on Proof-Theoretic Semantics.Thomas Piecha & Kai Wehmeier (eds.) - 2024 - Springer.
    This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy of language. -/- The chapters of which this book is composed discuss the (...)
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  2. The MultiAlist System of Thought (philosophical essay).Florentin Smarandache - 2023 - Neutrosophic Sets and Systems 61:598-605.
    The goal of this short note is to expand the concepts of ‘pluralism’, ‘neutrosophy’, ‘refined neutrosophy’, ‘refined neutrosophic set’, ‘multineutrosophic set’, and ‘plithogeny’ (Smarandache 2002, 2013, 2017, 2019, 2021, 2023a, 2023b, 2023c), into a larger category that I will refer to as MultiAlism (or MultiPolar). As a straightforward generalization, I propose the conceptualization of a MultiPolar System (different from a PluriPolar System), which is formed not only by multiple elements that might be random, or contradictory, or adjuvant, but also by (...)
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  3. The Palgrave Companion to the Philosophy of Set Theory.Carolin Antos, Neil Barton & Giorgio Venturi (eds.) - forthcoming - Palgrave.
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  4. The hidden use of new axioms.Deborah Kant - 2023 - In Carolin Antos, Neil Barton & Giorgio Venturi (eds.), The Palgrave Companion to the Philosophy of Set Theory. Palgrave Macmillan.
    This paper analyses the hidden use of new axioms in set-theoretic practice with a focus on large cardinal axioms and presents a general overview of set-theoretic practices using large cardinal axioms. The hidden use of a new axiom provides extrinsic reasons in support of this axiom via the idea of verifiable consequences, which is especially relevant for set-theoretic practitioners with an absolutist view. Besides that, the hidden use has pragmatic significance for further important sub-groups of the set-theoretic community---set-theoretic practitioners with (...)
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  5. Against ‘Interpretation’: Quantum Mechanics Beyond Syntax and Semantics.Raoni Wohnrath Arroyo & Gilson Olegario da Silva - 2022 - Axiomathes 32 (6):1243-1279.
    The question “what is an interpretation?” is often intertwined with the perhaps even harder question “what is a scientific theory?”. Given this proximity, we try to clarify the first question to acquire some ground for the latter. The quarrel between the syntactic and semantic conceptions of scientific theories occupied a large part of the scenario of the philosophy of science in the 20th century. For many authors, one of the two currents needed to be victorious. We endorse that such debate, (...)
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  6. Expanding the notion of inconsistency in mathematics: the theoretical foundations of mutual inconsistency.Carolin Antos - forthcoming - From Contradiction to Defectiveness to Pluralism in Science: Philosophical and Formal Analyses.
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  7. Are Large Cardinal Axioms Restrictive?Neil Barton - 2023 - Philosophia Mathematica 31 (3):372-407.
    The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper I question this claim. I show that there is a kind of maximality (namely absoluteness) on which large cardinal axioms come out as restrictive relative to a formal notion of restrictiveness. Within this framework, I argue that large cardinal axioms can still play many of (...)
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  8. Extensional Realizability and Choice for Dependent Types in Intuitionistic Set Theory.Emanuele Frittaion - 2023 - Journal of Symbolic Logic 88 (3):1138-1169.
    In [17], we introduced an extensional variant of generic realizability [22], where realizers act extensionally on realizers, and showed that this form of realizability provides inner models of $\mathsf {CZF}$ (constructive Zermelo–Fraenkel set theory) and $\mathsf {IZF}$ (intuitionistic Zermelo–Fraenkel set theory), that further validate $\mathsf {AC}_{\mathsf {FT}}$ (the axiom of choice in all finite types). In this paper, we show that extensional generic realizability validates several choice principles for dependent types, all exceeding $\mathsf {AC}_{\mathsf {FT}}$. We then show that adding (...)
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  9. An overview of Conceptual Analysis and Design.Dmitry E. Borisoglebsky - 2023 - Knowledge - International Journal 57 (3):353–365.
    Conceptual Analysis and Design (mCAD) is an information and cognitive technology for knowledge and systems engineering. A conceptual system for a complex knowledge domain contains thousands of linked concepts, necessary in the engineering and management of big and complex systems. Naturally evolved conceptual systems usually contain conceptual gaps and have multiple logical fallacies. mCAD addresses these issues by axiomatic deduction of concepts. This article is a concise overview of Conceptual Analysis and Design, covering its foundations, technological aspects, and notable applications.
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  10. A beginner's guide to mathematical logic.Raymond M. Smullyan - 2014 - Mineola, New York: Dover Publications.
    Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate (...)
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  11. Concise introduction to logic and set theory.Iqbal H. Jebril - 2022 - Boca Raton: CRC Press, Taylor & Francis Group. Edited by Hemen Dutta & Ilwoo Cho.
    This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and set theory are required in many areas of physical sciences, engineering, and technology. The book offers solved examples and exercises, and provides reasonable details to each topic discussed, for easy understanding. The book is designed for (...)
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  12. Précis de philosophie: classes de mathématiques et de mathématiques-technique.Armand Cuvillier - 1954 - Paris,: A. Colin.
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  13. Almene begreber fra logik, mængdelære og algebra.Bent Christiansen - 1964 - [Copenhagen]: Munksgaard. Edited by Jonas Lichtenberg, Pedersen, Johs & [From Old Catalog].
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  14. What makes a `good' modal theory of sets?Neil Barton - manuscript
    I provide an examination and comparison of modal theories for underwriting different non-modal theories of sets. I argue that there is a respect in which the `standard' modal theory for set construction---on which sets are formed via the successive individuation of powersets---raises a significant challenge for some recently proposed `countabilist' modal theories (i.e. ones that imply that every set is countable). I examine how the countabilist can respond to this issue via the use of regularity axioms and raise some questions (...)
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  15. Book 5 — ӝ : A Treatise Towards a Robust Set Theoretic Ontology.Jacob Parr - manuscript
    The author solves open problems in ontology , set theory , mathematics , modal logic . The author details the ontological commitments and implications of said found solutions and proves the need for and provides the solution to a new fundamental theory of algebra ... The author also provides the correct pronunciation of "prima facie" , a means for remembering the correct pronunciation of "prima facie" — and suggests others adopt the correct pronunciation of -- it's fun to say the (...)
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  16. Set Theory with Urelements.Bokai Yao - 2023 - Dissertation, University of Notre Dame
    This dissertation aims to provide a comprehensive account of set theory with urelements. In Chapter 1, I present mathematical and philosophical motivations for studying urelement set theory and lay out the necessary technical preliminaries. Chapter 2 is devoted to the axiomatization of urelement set theory, where I introduce a hierarchy of axioms and discuss how ZFC with urelements should be axiomatized. The breakdown of this hierarchy of axioms in the absence of the Axiom of Choice is also explored. In Chapter (...)
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  17. Schopenhauers Logikdiagramme in den Mathematiklehrbüchern Adolph Diesterwegs.Jens Lemanski - 2022 - Siegener Beiträge Zur Geschichte Und Philosophie der Mathematik 16:97-127.
    Ein Beispiel für die Rezeption und Fortführung der schopenhauerschen Logik findet man in den Mathematiklehrbüchern Friedrich Adolph Wilhelm Diesterwegs (1790–1866), In diesem Aufsatz werden die historische und systematische Dimension dieser Anwendung von Logikdiagramme auf die Mathematik skizziert. In Kapitel 2 wird zunächst die frühe Rezeption der schopenhauerschen Logik und Philosophie der Mathematik vorgestellt. Dabei werden einige oftmals tradierte Vorurteile, die das Werk Schopenhauers betreffen, in Frage gestellt oder sogar ausgeräumt. In Kapitel 3 wird dann die Philosophie der Mathematik und der (...)
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  18. Reduction games, provability and compactness.Damir D. Dzhafarov, Denis R. Hirschfeldt & Sarah Reitzes - 2022 - Journal of Mathematical Logic 22 (3).
    Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. Hirschfeldt and Jockusch (2016) introduced a two-player game in which winning strategies for one or the other player precisely correspond to implications and non-implications between [math] principles over [math]-models of [math]. They also introduced a version of this game that similarly captures provability over [math]. We generalize and extend this game-theoretic framework to other formal systems, and establish a certain compactness result that shows that if an implication [math] between two (...)
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  19. Sigma-Prikry forcing II: Iteration Scheme.Alejandro Poveda, Assaf Rinot & Dima Sinapova - 2022 - Journal of Mathematical Logic 22 (3):2150019.
    In Part I of this series [A. Poveda, A. Rinot and D. Sinapova, Sigma-Prikry forcing I: The axioms, Canad. J. Math. 73(5) (2021) 1205–1238], we introduced a class of notions of forcing which we call [Formula: see text]-Prikry, and showed that many of the known Prikry-type notions of forcing that center around singular cardinals of countable cofinality are [Formula: see text]-Prikry. We showed that given a [Formula: see text]-Prikry poset [Formula: see text] and a [Formula: see text]-name for a non-reflecting (...)
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  20. Mathematical Modality: An Investigation of Set Theoretic Contingency.Andrew Bacon - forthcoming - Journal of Philosophical Logic.
    An increasing amount of contemporary philosophy of mathematics posits, and theorizes in terms of special kinds of mathematical modality. The goal of this paper is to bring recent work on higher-order metaphysics to bear on the investigation of these modalities. The main focus of the paper will be views that posit mathematical contingency or indeterminacy about statements that concern the `width' of the set theoretic universe, such as Cantor's continuum hypothesis. Within a higher-order framework I show that contingency about the (...)
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  21. Lower and Upper Estimates of the Quantity of Algebraic Numbers.Yaroslav Sergeyev - 2023 - Mediterranian Journal of Mathematics 20:12.
    It is well known that the set of algebraic numbers (let us call it A) is countable. In this paper, instead of the usage of the classical terminology of cardinals proposed by Cantor, a recently introduced methodology using ①-based infinite numbers is applied to measure the set A (where the number ① is called grossone). Our interest to this methodology is explained by the fact that in certain cases where cardinals allow one to say only whether a set is countable (...)
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  22. Extension of Soft Set to Hypersoft Set, and then to Plithogenic Hypersoft Set.Florentin Smarandache - 2018 - Neutrosophic Sets and Systems 22 (1):168-170.
    In this paper, we generalize the soft set to the hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.
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  23. Introduction to the Complex Refined Neutrosophic Set.Florentin Smarandache - 2017 - Critical Review: A Journal of Politics and Society 14 (1):5-9.
    In this paper, one extends the single-valued complex neutrosophic set to the subsetvalued complex neutrosophic set, and afterwards to the subset-valued complex refined neutrosophic set.
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  24. Realizing realizability results with classical constructions.Asaf Karagila - 2019 - Bulletin of Symbolic Logic 25 (4):429-445.
    J. L. Krivine developed a new method based on realizability to construct models of set theory where the axiom of choice fails. We attempt to recreate his results in classical settings, i.e., symmetric extensions. We also provide a new condition for preserving well ordered, and other particular type of choice, in the general settings of symmetric extensions.
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  25. MORRIS, Sean: Quine, New Foundations, and the Philosophy of Set Theory.Ádám Tamas Tuboly - 2019 - Filozofia 74 (6).
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  26. RETRACTED ARTICLE: The Twin Primes Conjecture is True in the Standard Model of Peano Arithmetic: Applications of Rasiowa–Sikorski Lemma in Arithmetic (I).Janusz Czelakowski - 2023 - Studia Logica 111 (2):357-358.
    The paper is concerned with the old conjecture that there are infinitely many twin primes. In the paper we show that this conjecture is true, that is, it is true in the standard model of arithmetic. The proof is based on Rasiowa–Sikorski Lemma. The key role are played by the derived notion of a Rasiowa–Sikorski set and the method of forcing adjusted to arbitrary first–order languages. This approach was developed in the papers Czelakowski [ 4, 5 ]. The central idea (...)
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  27. An axiomatic approach to forcing in a general setting.Rodrigo A. Freire & Peter Holy - 2022 - Bulletin of Symbolic Logic 28 (3):427-450.
    The technique of forcing is almost ubiquitous in set theory, and it seems to be based on technicalities like the concepts of genericity, forcing names and their evaluations, and on the recursively defined forcing predicates, the definition of which is particularly intricate for the basic case of atomic first order formulas. In his [3], the first author has provided an axiomatic framework for set forcing over models of $\mathrm {ZFC}$ that is a collection of guiding principles for extensions over which (...)
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  28. Logic and discrete mathematics: a concise introduction.Willem Conradie - 2015 - Hoboken, NJ, USA: Wiley. Edited by Valentin Goranko.
    A concise yet rigorous introduction to logic and discrete mathematics. This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. The chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical (...)
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  29. Four cardinals and their relations in ZF.Lorenz Halbeisen, Riccardo Plati, Salome Schumacher & Saharon Shelah - 2023 - Annals of Pure and Applied Logic 174 (2):103200.
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  30. A first course in mathematical logic and set theory.Michael L. O'Leary - 2016 - Hoboken, New Jersey: Wiley.
    Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems.
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  31. Basic discrete mathematics: logic, set theory, & probability.Richard Kohar - 2016 - New Jersey: World Scientific.
    This lively introductory text exposes the student in the humanities to the world of discrete mathematics. A problem-solving based approach grounded in the ideas of George Pólya are at the heart of this book. Students learn to handle and solve new problems on their own. A straightforward, clear writing style and well-crafted examples with diagrams invite the students to develop into precise and critical thinkers. Particular attention has been given to the material that some students find challenging, such as proofs. (...)
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  32. Principles of mathematics: a primer.Vladimir Lepetic - 2016 - Hoboken, New Jersey: Wiley.
    Set theory -- Logic -- Proofs -- Functions -- Group theory -- Linear algebra.
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  33. Model-Theoretic Properties of Dynamics on the Cantor Set.Christopher J. Eagle & Alan Getz - 2022 - Notre Dame Journal of Formal Logic 63 (3):357-371.
    We examine topological dynamical systems on the Cantor set from the point of view of the continuous model theory of commutative C*-algebras. After some general remarks, we focus our attention on the generic homeomorphism of the Cantor set, as constructed by Akin, Glasner, and Weiss. We show that this homeomorphism is the prime model of its theory. We also show that the notion of “generic” used by Akin, Glasner, and Weiss is distinct from the notion of “generic” encountered in Fraïssé (...)
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  34. Ontology and Arbitrariness.David Builes - 2022 - Australasian Journal of Philosophy 100 (3):485-495.
    In many different ontological debates, anti-arbitrariness considerations push one towards two opposing extremes. For example, in debates about mereology, one may be pushed towards a maximal ontology (mereological universalism) or a minimal ontology (mereological nihilism), because any intermediate view seems objectionably arbitrary. However, it is usually thought that anti-arbitrariness considerations on their own cannot decide between these maximal or minimal views. I will argue that this is a mistake. Anti-arbitrariness arguments may be used to motivate a certain popular thesis in (...)
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  35. A Reassessment of Cantorian Abstraction based on the $$\varepsilon $$ ε -operator.Nicola Bonatti - 2022 - Synthese 200 (5):1-26.
    Cantor’s abstractionist account of cardinal numbers has been criticized by Frege as a psychological theory of numbers which leads to contradiction. The aim of the paper is to meet these objections by proposing a reassessment of Cantor’s proposal based upon the set theoretic framework of Bourbaki—called BK—which is a First-order set theory extended with Hilbert’s \-operator. Moreover, it is argued that the BK system and the \-operator provide a faithful reconstruction of Cantor’s insights on cardinal numbers. I will introduce first (...)
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  36. Subcompact Cardinals, Type Omission, and Ladder Systems.Yair Hayut & Menachem Magidor - 2022 - Journal of Symbolic Logic 87 (3):1111-1129.
    We provide a model theoretical and tree property-like characterization of $\lambda $ - $\Pi ^1_1$ -subcompactness and supercompactness. We explore the behavior of these combinatorial principles at accessible cardinals.
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  37. Complexity of Index Sets of Descriptive Set-Theoretic Notions.Reese Johnston & Dilip Raghavan - 2022 - Journal of Symbolic Logic 87 (3):894-911.
    Descriptive set theory and computability theory are closely-related fields of logic; both are oriented around a notion of descriptive complexity. However, the two fields typically consider objects of very different sizes; computability theory is principally concerned with subsets of the naturals, while descriptive set theory is interested primarily in subsets of the reals. In this paper, we apply a generalization of computability theory, admissible recursion theory, to consider the relative complexity of notions that are of interest in descriptive set theory. (...)
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  38. Meager-Additive Sets in Topological Groups.Ondřej Zindulka - 2022 - Journal of Symbolic Logic 87 (3):1046-1064.
    By the Galvin–Mycielski–Solovay theorem, a subset X of the line has Borel’s strong measure zero if and only if $M+X\neq \mathbb {R}$ for each meager set M.A set $X\subseteq \mathbb {R}$ is meager-additive if $M+X$ is meager for each meager set M. Recently a theorem on meager-additive sets that perfectly parallels the Galvin–Mycielski–Solovay theorem was proven: A set $X\subseteq \mathbb {R}$ is meager-additive if and only if it has sharp measure zero, a notion akin to strong measure zero.We investigate the (...)
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  39. Descriptive Complexity in Cantor Series.Dylan Airey, Steve Jackson & Bill Mance - 2022 - Journal of Symbolic Logic 87 (3):1023-1045.
    A Cantor series expansion for a real number x with respect to a basic sequence $Q=(q_1,q_2,\dots )$, where $q_i \geq 2$, is a generalization of the base b expansion to an infinite sequence of bases. Ki and Linton in 1994 showed that for ordinary base b expansions the set of normal numbers is a $\boldsymbol {\Pi }^0_3$ -complete set, establishing the exact complexity of this set. In the case of Cantor series there are three natural notions of normality: normality, ratio (...)
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  40. The Turing Degrees and Keisler’s Order.Maryanthe Malliaris & Saharon Shelah - forthcoming - Journal of Symbolic Logic:1-11.
    There is a Turing functional $\Phi $ taking $A^\prime $ to a theory $T_A$ whose complexity is exactly that of the jump of A, and which has the property that $A \leq _T B$ if and only if $T_A \trianglelefteq T_B$ in Keisler’s order. In fact, by more elaborate means and related theories, we may keep the complexity at the level of A without using the jump.
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  41. Strong Compactness, Square, Gch, and Woodin Cardinals.Arthur W. Apter - forthcoming - Journal of Symbolic Logic:1-9.
    We show the consistency, relative to the appropriate supercompactness or strong compactness assumptions, of the existence of a non-supercompact strongly compact cardinal $\kappa _0$ (the least measurable cardinal) exhibiting properties which are impossible when $\kappa _0$ is supercompact. In particular, we construct models in which $\square _{\kappa ^+}$ holds for every inaccessible cardinal $\kappa $ except $\kappa _0$, GCH fails at every inaccessible cardinal except $\kappa _0$, and $\kappa _0$ is less than the least Woodin cardinal.
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  42. Mathematical Progress — On Maddy and Beyond.Simon Weisgerber - 2023 - Philosophia Mathematica 31 (1):1-28.
    A key question of the ‘maverick’ tradition of the philosophy of mathematical practice is addressed, namely what is mathematical progress. The investigation is based on an article by Penelope Maddy devoted to this topic in which she considers only contributions ‘of some mathematical importance’ as progress. With the help of a case study from contemporary mathematics, more precisely from tropical geometry, a few issues with her proposal are identified. Taking these issues into consideration, an alternative account of ‘mathematical importance’, broadly (...)
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  43. Cohen-like first order structures.Ziemowit Kostana - 2023 - Annals of Pure and Applied Logic 174 (1):103172.
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  44. Non-stationary support iterations of Prikry forcings and restrictions of ultrapower embeddings to the ground model.Moti Gitik & Eyal Kaplan - 2023 - Annals of Pure and Applied Logic 174 (1):103164.
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  45. The Poset of All Logics II: Leibniz Classes and Hierarchy.R. Jansana & T. Moraschini - 2023 - Journal of Symbolic Logic 88 (1):324-362.
    A Leibniz class is a class of logics closed under the formation of term-equivalent logics, compatible expansions, and non-indexed products of sets of logics. We study the complete lattice of all Leibniz classes, called the Leibniz hierarchy. In particular, it is proved that the classes of truth-equational and assertional logics are meet-prime in the Leibniz hierarchy, while the classes of protoalgebraic and equivalential logics are meet-reducible. However, the last two classes are shown to be determined by Leibniz conditions consisting of (...)
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  46. Incompatible bounded category forcing axioms.David Asperó & Matteo Viale - 2022 - Journal of Mathematical Logic 22 (2).
    Journal of Mathematical Logic, Volume 22, Issue 02, August 2022. We introduce bounded category forcing axioms for well-behaved classes [math]. These are strong forms of bounded forcing axioms which completely decide the theory of some initial segment of the universe [math] modulo forcing in [math], for some cardinal [math] naturally associated to [math]. These axioms naturally extend projective absoluteness for arbitrary set-forcing — in this situation [math] — to classes [math] with [math]. Unlike projective absoluteness, these higher bounded category forcing (...)
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  47. Forcing the [math]-separation property.Stefan Hoffelner - 2022 - Journal of Mathematical Logic 22 (2).
    Journal of Mathematical Logic, Volume 22, Issue 02, August 2022. We generically construct a model in which the [math]-separation property is true, i.e. every pair of disjoint [math]-sets can be separated by a [math]-definable set. This answers an old question from the problem list “Surrealist landscape with figures” by A. Mathias from 1968. We also construct a model in which the (lightface) [math]-separation property is true.
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  48. Structural reflection, shrewd cardinals and the size of the continuum.Philipp Lücke - 2022 - Journal of Mathematical Logic 22 (2).
    Journal of Mathematical Logic, Volume 22, Issue 02, August 2022. Motivated by results of Bagaria, Magidor and Väänänen, we study characterizations of large cardinal properties through reflection principles for classes of structures. More specifically, we aim to characterize notions from the lower end of the large cardinal hierarchy through the principle [math] introduced by Bagaria and Väänänen. Our results isolate a narrow interval in the large cardinal hierarchy that is bounded from below by total indescribability and from above by subtleness, (...)
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  49. The permutations with N_ non-fixed points and the sequences with length _N of a set.Jukkrid Nuntasri & Pimpen Vejjajiva - forthcoming - Journal of Symbolic Logic:1-10.
    We write$\mathcal {S}_n(A)$for the set of permutations of a setAwithnnon-fixed points and$\mathrm {{seq}}^{1-1}_n(A)$for the set of one-to-one sequences of elements ofAwith lengthnwherenis a natural number greater than$1$. With the Axiom of Choice,$|\mathcal {S}_n(A)|$and$|\mathrm {{seq}}^{1-1}_n(A)|$are equal for all infinite setsA. Among our results, we show, in ZF, that$|\mathcal {S}_n(A)|\leq |\mathrm {{seq}}^{1-1}_n(A)|$for any infinite setAif${\mathrm {AC}}_{\leq n}$is assumed and this assumption cannot be removed. In the other direction, we show that$|\mathrm {{seq}}^{1-1}_n(A)|\leq |\mathcal {S}_{n+1}(A)|$for any infinite setAand the subscript$n+1$cannot be reduced ton. Moreover, (...)
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  50. Constructive strong regularity and the extension property of a compactification.Giovanni Curi - 2023 - Annals of Pure and Applied Logic 174 (1):103154.
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