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  1.  18
    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 Smoryński'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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  2.  12
    Closed Normal Subgroups of the Automorphism Group of a Saturated Model of Peano Arithmetic.Ermek S. Nurkhaidarov & Erez Shochat - 2016 - Notre Dame Journal of Formal Logic 57 (1):127-139.
    In this paper we discuss automorphism groups of saturated models and boundedly saturated models of $\mathsf{PA}$. We show that there are saturated models of $\mathsf{PA}$ of the same cardinality with nonisomorphic automorphism groups. We then show that every saturated model of $\mathsf{PA}$ has short saturated elementary cuts with nonisomorphic automorphism groups.
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  3.  20
    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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  4.  8
    A Galois Correspondence for Countable Short Recursively Saturated Models of PA.Erez Shochat - 2010 - Mathematical Logic Quarterly 56 (3):228-238.
    In this paper we investigate the properties of automorphism groups of countable short recursively saturated models of arithmetic. In particular, we show that Kaye's Theorem concerning the closed normal subgroups of automorphism groups of countable recursively saturated models of arithmetic applies to automorphism groups of countable short recursively saturated models as well. That is, the closed normal subgroups of the automorphism group of a countable short recursively saturated model of PA are exactly the stabilizers of the invariant cuts of the (...)
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