5 found
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  1.  2
    Largest Initial Segments Pointwise Fixed by Automorphisms of Models of Set Theory.Ali Enayat, Matt Kaufmann & Zachiri McKenzie - 2018 - Archive for Mathematical Logic 57 (1-2):91-139.
    Given a model \ of set theory, and a nontrivial automorphism j of \, let \\) be the submodel of \ whose universe consists of elements m of \ such that \=x\) for every x in the transitive closure of m ). Here we study the class \ of structures of the form \\), where the ambient model \ satisfies a frugal yet robust fragment of \ known as \, and \=m\) whenever m is a finite ordinal in the sense (...)
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  2.  3
    Automorphisms of Models of Set Theory and Extensions of NFU.Zachiri McKenzie - 2015 - Annals of Pure and Applied Logic 166 (5):601-638.
  3.  3
    Iterated Ultrapowers for the Masses.Ali Enayat, Matt Kaufmann & Zachiri McKenzie - 2018 - Archive for Mathematical Logic 57 (5-6):557-576.
    We present a novel, perspicuous framework for building iterated ultrapowers. Furthermore, our framework naturally lends itself to the construction of a certain type of order indiscernibles, here dubbed tight indiscernibles, which are shown to provide smooth proofs of several results in general model theory.
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  4.  5
    Decidable Fragments of the Simple Theory of Types with Infinity and $Mathrm{NF}$.Anuj Dawar, Thomas Forster & Zachiri McKenzie - 2017 - Notre Dame Journal of Formal Logic 58 (3):433-451.
    We identify complete fragments of the simple theory of types with infinity and Quine’s new foundations set theory. We show that TSTI decides every sentence ϕ in the language of type theory that is in one of the following forms: ϕ=∀x1r1⋯∀xkrk∃y1s1⋯∃ylslθ where the superscripts denote the types of the variables, s1>⋯>sl, and θ is quantifier-free, ϕ=∀x1r1⋯∀xkrk∃y1s⋯∃ylsθ where the superscripts denote the types of the variables and θ is quantifier-free. This shows that NF decides every stratified sentence ϕ in the language (...)
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  5.  4
    On the Strength of a Weak Variant of the Axiom of Counting.Zachiri McKenzie - 2017 - Mathematical Logic Quarterly 63 (1-2):94-103.
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