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  1. Automorphisms of Countable Short Recursively Saturated Models of PA.Erez Shochat - 2008 - Notre Dame Journal of Formal Logic 49 (4):345-360.
    A model of Peano Arithmetic is short recursively saturated if it realizes all its bounded finitely realized recursive types. Short recursively saturated models of $\PA$ are exactly the elementary initial segments of recursively saturated models of $\PA$. In this paper, we survey and prove results on short recursively saturated models of $\PA$ and their automorphisms. In particular, we investigate a certain subgroup of the automorphism group of such models. This subgroup, denoted $G|_{M(a)}$, contains all the automorphisms of a countable short (...)
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  • Automorphisms of Saturated and Boundedly Saturated Models of Arithmetic.Ermek S. Nurkhaidarov & Erez Shochat - 2011 - Notre Dame Journal of Formal Logic 52 (3):315-329.
    We discuss automorphisms of saturated models of PA and boundedly saturated models of PA. We show that SmoryƄski's Lemma and Kaye's Theorem are not only true for countable recursively saturated models of PA but also true for all boundedly saturated models of PA with slight modifications.
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  • Automorphisms of Countable Recursively Saturated Models of PA: A Survey.Henryk Kotlarski - 1995 - Notre Dame Journal of Formal Logic 36 (4):505-518.
    We give a survey of automorphisms of countable recursively saturated models of Peano Arithmetic.
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  • Automorphisms of Models of True Arithmetic: Recognizing Some Basic Open Subgroups.Henryk Kotlarski & Richard Kaye - 1994 - Notre Dame Journal of Formal Logic 35 (1):1-14.
    Let M be a countable recursively saturated model of Th(), and let GAut(M), considered as a topological group. We examine connections between initial segments of M and subgroups of G. In particular, for each of the following classes of subgroups HG, we give characterizations of the class of terms of the topological group structure of H as a subgroup of G. (a) for some (b) for some (c) for some (d) for some (Here, M(a) denotes the smallest M containing a, (...)
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  • 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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