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  1.  17
    Automorphism Groups of Arithmetically Saturated Models.Ermek S. Nurkhaidarov - 2006 - Journal of Symbolic Logic 71 (1):203 - 216.
    In this paper we study the automorphism groups of countable arithmetically saturated models of Peano Arithmetic. The automorphism groups of such structures form a rich class of permutation groups. When studying the automorphism group of a model, one is interested to what extent a model is recoverable from its automorphism group. Kossak-Schmerl [12] show that ifMis a countable, arithmetically saturated model of Peano Arithmetic, then Aut(M) codes SSy(M). Using that result they prove:Let M1. M2be countable arithmetically saturated models of Peano (...)
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  2.  9
    Automorphism Groups of Saturated Models of Peano Arithmetic.Ermek S. Nurkhaidarov & James H. Schmerl - 2014 - Journal of Symbolic Logic 79 (2):561-584.
    Letκbe the cardinality of some saturated model of Peano Arithmetic. There is a set of${2^{{\aleph _0}}}$saturated models of PA, each having cardinalityκ, such that wheneverMandNare two distinct models from this set, then Aut(${\cal M}$) ≇ Aut ($${\cal N}$$).
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  3.  29
    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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  4.  20
    Interstitial and pseudo gaps in models of Peano Arithmetic.Ermek S. Nurkhaidarov - 2010 - Mathematical Logic Quarterly 56 (2):198-204.
    In this paper we study the automorphism groups of models of Peano Arithmetic. Kossak, Kotlarski, and Schmerl [9] shows that the stabilizer of an unbounded element a of a countable recursively saturated model of Peano Arithmetic M is a maximal subgroup of Aut if and only if the type of a is selective. We extend this result by showing that if M is a countable arithmetically saturated model of Peano Arithmetic, Ω ⊂ M is a very good interstice, and a (...)
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  5.  16
    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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