20 found

View year:

  1.  43
    John MacFarlane, Philosophical Logic: A Contemporary Introduction, Routledge Contemporary Introductions to Philosophy, Routledge, New York, and London, 2021, xx + 238 pp. [REVIEW]Bruno Bentzen - 2023 - Bulletin of Symbolic Logic 29 (3):456-457.
  2.  5
    A Classical Modal Theory of Lawless Sequences.Ethan Brauer - 2023 - Bulletin of Symbolic Logic 29 (3):406-452.
    Free choice sequences play a key role in the intuitionistic theory of the continuum and especially in the theorems of intuitionistic analysis that conflict with classical analysis, leading many classical mathematicians to reject the concept of a free choice sequence. By treating free choice sequences as potentially infinite objects, however, they can be comfortably situated alongside classical analysis, allowing a rapprochement of these two mathematical traditions. Building on recent work on the modal analysis of potential infinity, I formulate a modal (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  3.  17
    Extended Frames and Separations of Logical Principles.Makoto Fujiwara, Hajime Ishihara, Takako Nemoto, Nobu-Yuki Suzuki & Keita Yokoyama - 2023 - Bulletin of Symbolic Logic 29 (3):311-353.
    We aim at developing a systematic method of separating omniscience principles by constructing Kripke models for intuitionistic predicate logic $\mathbf {IQC}$ and first-order arithmetic $\mathbf {HA}$ from a Kripke model for intuitionistic propositional logic $\mathbf {IPC}$. To this end, we introduce the notion of an extended frame, and show that each IPC-Kripke model generates an extended frame. By using the extended frame generated by an IPC-Kripke model, we give a separation theorem of a schema from a set of schemata in (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  4.  7
    Menas’s Conjecture Revisited.Pierre Matet - 2023 - Bulletin of Symbolic Logic 29 (3):354-405.
    In an article published in 1974, Menas conjectured that any stationary subset of can be split in many pairwise disjoint stationary subsets. Even though the conjecture was shown long ago by Baumgartner and Taylor to be consistently false, it is still haunting papers on. In which situations does it hold? How much of it can be proven in ZFC? We start with an abridged history of the conjecture, then we formulate a new version of it, and finally we keep weakening (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  5.  18
    THREE PAPERS ON RECENT WORK ON META-VALIDITY - David Ripley, One step is enough_. Journal of Philosophical Logic, vol. 51 (2022), pp. 1233–1259. - Isabella McAllister, _Classical logic is not uniquely characterizable_. Journal of Philosophical Logic, vol. 51 (2022), pp. 1345–1365. - Rea Golan, _There is no tenable notion of global metainferential validity. Analysis, vol. 81 (2021), no. 3, pp. 411–420. [REVIEW]Chris Scambler - 2023 - Bulletin of Symbolic Logic 29 (3):453-456.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  6.  8
    Forcing theory and combinatorics of the real line.Miguel Antonio Cardona-Montoya - 2023 - Bulletin of Symbolic Logic 29 (2):299-300.
    The main purpose of this dissertation is to apply and develop new forcing techniques to obtain models where several cardinal characteristics are pairwise different as well as force many (even more, continuum many) different values of cardinal characteristics that are parametrized by reals. In particular, we look at cardinal characteristics associated with strong measure zero, Yorioka ideals, and localization and anti-localization cardinals.In this thesis we introduce the property “F-linked” of subsets of posets for a given free filter F on the (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  7.  10
    Computably Compact Metric Spaces.Rodney G. Downey & Alexander G. Melnikov - 2023 - Bulletin of Symbolic Logic 29 (2):170-263.
    We give a systematic technical exposition of the foundations of the theory of computably compact metric spaces. We discover several new characterizations of computable compactness and apply these characterizations to prove new results in computable analysis and effective topology. We also apply the technique of computable compactness to give new and less combinatorially involved proofs of known results from the literature. Some of these results do not have computable compactness or compact spaces in their statements, and thus these applications are (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  8.  30
    Katie Steele and H. Orri Stefánsson. Beyond Uncertainty: Reasoning with Unknown Possibilities. Elements in Decision Theory and Philosophy. Cambridge University Press, Cambridge, UK, 2021, 110 pp. [REVIEW]Magdalen Elmitt - 2023 - Bulletin of Symbolic Logic 29 (2):294-296.
  9.  5
    Incompatibility of Generic Hugeness Principles.Monroe Eskew - 2023 - Bulletin of Symbolic Logic 29 (2):157-162.
    We show that the weakest versions of Foreman’s minimal generic hugeness axioms cannot hold simultaneously on adjacent cardinals. Moreover, conventional forcing techniques cannot produce a model of one of these axioms.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  10.  4
    Around Exponential-Algebraic Closedness.Francesco Paolo Gallinaro - 2023 - Bulletin of Symbolic Logic 29 (2):300-300.
    We present some results related to Zilber’s Exponential-Algebraic Closedness Conjecture, showing that various systems of equations involving algebraic operations and certain analytic functions admit solutions in the complex numbers. These results are inspired by Zilber’s theorems on raising to powers.We show that algebraic varieties which split as a product of a linear subspace of an additive group and an algebraic subvariety of a multiplicative group intersect the graph of the exponential function, provided that they satisfy Zilber’s freeness and rotundity conditions, (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  11.  4
    Saturated Models for the Working Model Theorist.Yatir Halevi & Itay Kaplan - 2023 - Bulletin of Symbolic Logic 29 (2):163-169.
    We put in print a classical result that states that for most purposes, there is no harm in assuming the existence of saturated models in model theory. The presentation is aimed for model theorists with only basic knowledge of axiomatic set theory.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  12.  13
    Under Lock and Key: A Proof System for a Multimodal Logic.G. A. Kavvos & Daniel Gratzer - 2023 - Bulletin of Symbolic Logic 29 (2):264-293.
    We present a proof system for a multimode and multimodal logic, which is based on our previous work on modal Martin-Löf type theory. The specification of modes, modalities, and implications between them is given as a mode theory, i.e., a small 2-category. The logic is extended to a lambda calculus, establishing a Curry–Howard correspondence.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  13.  14
    New methods in forcing iteration and applications.Rahman Mohammadpour - 2023 - Bulletin of Symbolic Logic 29 (2):300-302.
    The Theme. Strong forcing axioms like Martin’s Maximum give a reasonably satisfactory structural analysis of $H(\omega _2)$. A broad program in modern Set Theory is searching for strong forcing axioms beyond $\omega _1$. In other words, one would like to figure out the structural properties of taller initial segments of the universe. However, the classical techniques of forcing iterations seem unable to bypass the obstacles, as the resulting forcings axioms beyond $\omega _1$ have not thus far been strong enough! However, (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  14.  9
    Jan Krajìček, Proof Complexity, Encyclopedia of Mathematics and Its Applications, no. 170, Cambridge University Press, Cambridge, UK, 2019, xvi + 516 pp. [REVIEW]Moritz Müller - 2023 - Bulletin of Symbolic Logic 29 (2):296-297.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  15.  6
    Effective Concept Classes of PAC and PACi Incomparable Degrees, Joins and Embedding of Degrees.Dodamgodage Gihanee M. Senadheera - 2023 - Bulletin of Symbolic Logic 29 (2):298-299.
    The Probably Approximately Correct (PAC) learning is a machine learning model introduced by Leslie Valiant in 1984. The PACi reducibility refers to the PAC reducibility independent of size and computation time. This reducibility in PAC learning resembles the reducibility in Turing computability. The ordering of concept classes under PAC reducibility is nonlinear, even when restricted to particular concrete examples.Due to the resemblance to Turing Reducibility, we suspected that there could be incomparable PACi and PAC degrees for the PACi and PAC (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  16.  14
    On Double-Membership Graphs of Models of Anti-Foundation.Bea Adam-day, John Howe & Rosario Mennuni - 2023 - Bulletin of Symbolic Logic 29 (1):128-144.
    We answer some questions about graphs that are reducts of countable models of Anti-Foundation, obtained by considering the binary relation of double-membership $x\in y\in x$. We show that there are continuum-many such graphs, and study their connected components. We describe their complete theories and prove that each has continuum-many countable models, some of which are not reducts of models of Anti-Foundation.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  17.  10
    Large Cardinals as Principles of Structural Reflection.Joan Bagaria - 2023 - Bulletin of Symbolic Logic 29 (1):19-70.
    After discussing the limitations inherent to all set-theoretic reflection principles akin to those studied by A. Lévy et. al. in the 1960s, we introduce new principles of reflection based on the general notion of Structural Reflection and argue that they are in strong agreement with the conception of reflection implicit in Cantor’s original idea of the unknowability of the Absolute, which was subsequently developed in the works of Ackermann, Lévy, Gödel, Reinhardt, and others. We then present a comprehensive survey of (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  18.  3
    Which Classes of Structures Are Both Pseudo-Elementary and Definable by an Infinitary Sentence?Will Boney, Barbara F. Csima, D. A. Y. Nancy A. & Matthew Harrison-Trainor - 2023 - Bulletin of Symbolic Logic 29 (1):1-18.
    When classes of structures are not first-order definable, we might still try to find a nice description. There are two common ways for doing this. One is to expand the language, leading to notions of pseudo-elementary classes, and the other is to allow infinite conjuncts and disjuncts. In this paper we examine the intersection. Namely, we address the question: Which classes of structures are both pseudo-elementary and ${\mathcal {L}}_{\omega _1, \omega }$ -elementary? We find that these are exactly the classes (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  19.  6
    Constructing Nonstandard Hulls and Loeb Measures in Internal Set Theories.Karel Hrbacek & Mikhail G. Katz - 2023 - Bulletin of Symbolic Logic 29 (1):97-127.
    Currently the two popular ways to practice Robinson’s nonstandard analysis are the model-theoretic approach and the axiomatic/syntactic approach. It is sometimes claimed that the internal axiomatic approach is unable to handle constructions relying on external sets. We show that internal frameworks provide successful accounts of nonstandard hulls and Loeb measures. The basic fact this work relies on is that the ultrapower of the standard universe by a standard ultrafilter is naturally isomorphic to a subuniverse of the internal universe.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  20.  88
    The Axiom of Choice is False Intuitionistically (in Most Contexts).Charles Mccarty, Stewart Shapiro & Ansten Klev - 2023 - Bulletin of Symbolic Logic 29 (1):71-96.
    There seems to be a view that intuitionists not only take the Axiom of Choice (AC) to be true, but also believe it a consequence of their fundamental posits. Widespread or not, this view is largely mistaken. This article offers a brief, yet comprehensive, overview of the status of AC in various intuitionistic and constructivist systems. The survey makes it clear that the Axiom of Choice fails to be a theorem in most contexts and is even outright false in some (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
 Previous issues
  
Next issues