12 found
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  1.  6
    There Are No Intermediate Structures Between the Group of Integers and Presburger Arithmetic.Gabriel Conant - 2018 - Journal of Symbolic Logic 83 (1):187-207.
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  2.  13
    Forking and Dividing in Henson Graphs.Gabriel Conant - 2017 - Notre Dame Journal of Formal Logic 58 (4):555-566.
    For n≥3, define Tn to be the theory of the generic Kn-free graph, where Kn is the complete graph on n vertices. We prove a graph-theoretic characterization of dividing in Tn and use it to show that forking and dividing are the same for complete types. We then give an example of a forking and nondividing formula. Altogether, Tn provides a counterexample to a question of Chernikov and Kaplan.
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  3.  12
    An Axiomatic Approach to Free Amalgamation.Gabriel Conant - 2017 - Journal of Symbolic Logic 82 (2):648-671.
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  4.  16
    Independence in Generic Incidence Structures.Gabriel Conant & Alex Kruckman - 2019 - Journal of Symbolic Logic 84 (2):750-780.
  5.  15
    Remarks on Generic Stability in Independent Theories.Gabriel Conant & Kyle Gannon - 2020 - Annals of Pure and Applied Logic 171 (2):102736.
    In NIP theories, generically stable Keisler measures can be characterized in several ways. We analyze these various forms of “generic stability” in arbitrary theories. Among other things, we show that the standard definition of generic stability for types coincides with the notion of a frequency interpretation measure. We also give combinatorial examples of types in NSOP theories that are finitely approximated but not generically stable, as well as ϕ-types in simple theories that are definable and finitely satisfiable in a small (...)
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  6.  7
    Model Theoretic Properties of the Urysohn Sphere.Gabriel Conant & Caroline Terry - 2016 - Annals of Pure and Applied Logic 167 (1):49-72.
  7.  7
    Weakly Minimal Groups with a New Predicate.Gabriel Conant & Michael C. Laskowski - 2020 - Journal of Mathematical Logic 20 (2):2050011.
    Fix a weakly minimal (i.e. superstable U-rank 1) structure M. Let M∗ be an expansion by constants for an elementary substructure, and let A be an arbitrary subset of the universe M. We show that all formulas in the expansion (M∗,A) are equivalent to bounded formulas, and so (M,A) is stable (or NIP) if and only if the M-induced structure AM on A is stable (or NIP). We then restrict to the case that M is a pure abelian group with (...)
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  8.  7
    Neostability in Countable Homogeneous Metric Spaces.Gabriel Conant - 2017 - Annals of Pure and Applied Logic 168 (7):1442-1471.
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  9.  23
    Distance Structures for Generalized Metric Spaces.Gabriel Conant - 2017 - Annals of Pure and Applied Logic 168 (3):622-650.
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  10.  10
    A Remark on Strict Independence Relations.Gabriel Conant - 2016 - Archive for Mathematical Logic 55 (3-4):535-544.
    We prove that if T is a complete theory with weak elimination of imaginaries, then there is an explicit bijection between strict independence relations for T and strict independence relations for Teq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T^{\rm eq}}$$\end{document}. We use this observation to show that if T is the theory of the Fraïssé limit of finite metric spaces with integer distances, then Teq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T^{\rm eq}}$$\end{document} has more than one (...)
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  11. Associativity of the Morley Product of Invariant Measures in Nip Theories.Gabriel Conant & Kyle Gannon - 2021 - Journal of Symbolic Logic 86 (3):1293-1300.
    In light of a gap found by Krupiński, we give a new proof of associativity for the Morley product of invariant measures in NIP theories.
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  12.  2
    Pseudofinite Groups and VC-Dimension.Gabriel Conant & Anand Pillay - 2020 - Journal of Mathematical Logic 21 (2):2150009.
    We develop “local NIP group theory” in the context of pseudofinite groups. In particular, given a sufficiently saturated pseudofinite structure G expanding a group, and left invariant NIP formula δ...
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