Year:

  1.  35
    Large Cardinals Beyond Choice.Joan Bagaria, Peter Koellner & W. Hugh Woodin - 2019 - Bulletin of Symbolic Logic 25 (3):283-318.
    The HOD Dichotomy Theorem states that if there is an extendible cardinal, δ, then either HOD is “close” to V or HOD is “far” from V. The question is whether the future will lead to the first or the second side of the dichotomy. Is HOD “close” to V, or “far” from V? There is a program aimed at establishing the first alternative—the “close” side of the HOD Dichotomy. This is the program of inner model theory. In recent years the (...)
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  2.  10
    N. Francez, Proof-Theoretic Semantics, Studies in Logic, Vol. 57, College Publications, London, 2015, Xx + 415 Pp. [REVIEW]Davide Catta - 2019 - Bulletin of Symbolic Logic 25 (3):360-362.
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  3.  18
    Model Theory and Machine Learning.Hunter Chase & James Freitag - 2019 - Bulletin of Symbolic Logic 25 (3):319-332.
    About 25 years ago, it came to light that a single combinatorial property determines both an important dividing line in model theory and machine learning. The following years saw a fruitful exchange of ideas between PAC-learning and the model theory of NIP structures. In this article, we point out a new and similar connection between model theory and machine learning, this time developing a correspondence between stability and learnability in various settings of online learning. In particular, this gives many new (...)
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  4.  15
    Eta-Rules in Martin-Löf Type Theory.Ansten Klev - 2019 - Bulletin of Symbolic Logic 25 (3):333-359.
    The eta rule for a set A says that an arbitrary element of A is judgementally identical to an element of constructor form. Eta rules are not part of what may be called canonical Martin-Löf type theory. They are, however, justified by the meaning explanations, and a higher-order eta rule is part of that type theory. The main aim of this paper is to clarify this somewhat puzzling situation. It will be argued that lower-order eta rules do not, whereas the (...)
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  5.  4
    Self-Embeddings of Models of Peano Arithmetic.Saeideh Bahrami - 2019 - Bulletin of Symbolic Logic 25 (2):217-218.
  6.  15
    Foundations of Online Structure Theory.Nikolay Bazhenov, Rod Downey, Iskander Kalimullin & Alexander Melnikov - 2019 - Bulletin of Symbolic Logic 25 (2):141-181.
    The survey contains a detailed discussion of methods and results in the new emerging area of online “punctual” structure theory. We also state several open problems.
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  7.  7
    A Theory of Stationary Trees and the Balanced Baumgartner–Hajnal–Todorcevic Theorem for Trees.Ari Meir Brodsky - 2019 - Bulletin of Symbolic Logic 25 (2):219-219.
  8.  3
    Regular Tree Languages in the First Two Levels of the Borel Hierarchy.Filippo Cavallari - 2019 - Bulletin of Symbolic Logic 25 (2):221-222.
    The thesis focuses on a quite recent research field lying in between Descriptive Set Theory and Automata Theory (for infinite objects). In both areas, one is often concerned with subsets of the Cantor space or of its homeomorphic copies. In Descriptive Set Theory, such subsets are usually stratified in topological hierarchies, like the Borel hierarchy, the Wadge hierarchy and the difference hierarchy; in Automata Theory, such sets are studied in terms of regularity, that is, the property of being recognised by (...)
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  9.  10
    Indirect Proof and Inversions of Syllogisms.Roy Dyckhoff - 2019 - Bulletin of Symbolic Logic 25 (2):196-207.
    By considering the new notion of the inverses of syllogisms such as Barbara and Celarent, we show how the rule of Indirect Proof, in the form used by Aristotle, may be dispensed with, in a system comprising four basic rules of subalternation or conversion and six basic syllogisms.
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  10.  8
    Self-Similarity in the Foundations.Paul K. Gorbow - 2019 - Bulletin of Symbolic Logic 25 (2):216-217.
  11.  13
    A Conjectural Classification of Strongly Dependent Fields.Yatir Halevi, Assaf Hasson & Franziska Jahnke - 2019 - Bulletin of Symbolic Logic 25 (2):182-195.
    We survey the history of Shelah’s conjecture on strongly dependent fields, give an equivalent formulation in terms of a classification of strongly dependent fields and prove that the conjecture implies that every strongly dependent field has finite dp-rank.
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  12.  5
    Creatures and Cardinals.Lukas Daniel Klausner - 2019 - Bulletin of Symbolic Logic 25 (2):218-219.
  13.  8
    Vaught’s Two-Cardinal Theorem and Notions of Minimality in Continuous Logic.Victoria Noquez - 2019 - Bulletin of Symbolic Logic 25 (2):215-216.
  14.  13
    Explicit Computational Paths in Type Theory.Arthur Freitas Ramos - 2019 - Bulletin of Symbolic Logic 25 (2):213-214.
  15.  8
    Formalization of Context-Free Language Theory.Marcus Vinícius Midena Ramos - 2019 - Bulletin of Symbolic Logic 25 (2):214-214.
    Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different such tools are being increasingly used in order to accelerate and simplify proof checking, and the Coq proof assistant is one of the most well known and used in large-scale projects. Language and automata theory is a well-established area of mathematics, relevant to computer science foundations and information technology. In particular, context-free language (...)
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  16.  5
    Completeness of Finite-Rank Differential Varieties.William D. Simmons - 2019 - Bulletin of Symbolic Logic 25 (2):220-221.
  17.  17
    New Directions for Neo-Logicism.Aaron Thomas-Bolduc - 2019 - Bulletin of Symbolic Logic 25 (2):219-220.
  18.  5
    Some Applications of Set Theory to Model Theory.Douglas Ulrich - 2019 - Bulletin of Symbolic Logic 25 (2):214-215.
  19.  15
    An Extension of a Theorem of Zermelo.Jouko Väänänen - 2019 - Bulletin of Symbolic Logic 25 (2):208-212.
    We show that if $$ satisfies the first-order Zermelo–Fraenkel axioms of set theory when the membership relation is ${ \in _1}$ and also when the membership relation is ${ \in _2}$, and in both cases the formulas are allowed to contain both ${ \in _1}$ and ${ \in _2}$, then $\left \cong \left$, and the isomorphism is definable in $$. This extends Zermelo’s 1930 theorem in [6].
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  20.  11
    J. H. Schmerl, Subsets Coded in Elementary End Extensions. Archive for Mathematical Logic, Vol. 53 , No. 5–6, Pp. 571–581. - J. H. Schmerl, Minimal Elementary End Extensions. Archive for Mathematical Logic, Vol. 56 , No. 5–6, Pp. 541–553. [REVIEW]Athar Abdul-Quader - 2019 - Bulletin of Symbolic Logic 25 (1):125-126.
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  21.  6
    Henkin Constructions of Models with Size Continuum.John T. Baldwin & Michael C. Laskowski - 2019 - Bulletin of Symbolic Logic 25 (1):1-33.
    We describe techniques for constructing models of size continuum inωsteps by simultaneously building a perfect set of enmeshed countable Henkin sets. Such models have perfect, asymptotically similar subsets. We survey applications involving Borel models, atomic models, two-cardinal transfers and models respecting various closure relations.
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  22.  14
    Nominalistic Ordinals, Recursion on Higher Types, and Finitism.Maria Hämeen-Anttila - 2019 - Bulletin of Symbolic Logic 25 (1):101-124.
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  23.  17
    An Invitation to Model Theory and C*-Algebras.Martino Lupini - 2019 - Bulletin of Symbolic Logic 25 (1):34-100.
    We present an introductory survey to first order logic for metric structures and its applications to C*-algebras.
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