Source: Notre Dame J. Formal Logic
Volume 52, Number 3
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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 Blass, A., "The intersection of nonstandard models of arithmetic", The Journal of Symbolic Logic, vol. 37 (1972), pp. 103–6.
 Gaifman, H., "Models and types of Peano's arithmetic", Annals of Pure and Applied Logic, vol. 9 (1976), pp. 223–306.
 Kaye, R., Models of Peano Arithmetic, vol. 15 of Oxford Logic Guides, The Clarendon Press, New York, 1991.
 Kaye, R., "A Galois correspondence for countable recursively saturated models of Peano Arithmetic", pp. 293–312 in Automorphisms of First-Order Structures, Oxford Science Publications, Oxford University Press, New York, 1994.
 Kaye, R., R. Kossak, and H. Kotlarski, "Automorphisms of recursively saturated models of arithmetic", Annals of Pure and Applied Logic, vol. 55 (1991), pp. 67–99.
 Kossak, R., H. Kotlarski, and J. H. Schmerl, "On maximal subgroups of the automorphism group of a countable recursively saturated model of PA", Annals of Pure and Applied Logic, vol. 65 (1993), pp. 125–48.
 Kossak, R., and J. H. Schmerl, The Structure of Models of Peano Arithmetic, vol. 50 of Oxford Logic Guides, The Clarendon Press, New York, 2006.
 Kotlarski, H., "On elementary cuts in recursively saturated models of Peano Arithmetic", Fundamenta Mathematicae, vol. 120 (1984), pp. 205–22.
Mathematical Reviews (MathSciNet): MR755777
 Nurkhaidarov, E. S., "Automorphism groups of saturated models of PA" of cardinality $\aleph_1$, Collected Works Devoted to the Memory of A. D. Taimanov, (2006), pp. 295–97.
 Pabion, J.-F., "Saturated models of Peano arithmetic", The Journal of Symbolic Logic, vol. 47 (1982), pp. 625–37.
Mathematical Reviews (MathSciNet): MR666820
 Schmerl, J. H., "Closed normal subgroups", Mathematical Logic Quarterly, vol. 47 (2001), pp. 489–92.
 Shochat, E., "Automorphisms of countable short recursively saturated models of PA", Notre Dame Journal of Formal Logic, vol. 49 (2008), pp. 345–60.
 Smoryński, C., "Back-and-forth inside a recursively saturated model of arithmetic", pp. 273–78 in Logic Colloquium '80 (Prague, 1980), vol. 108 of Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1982.
Mathematical Reviews (MathSciNet): MR673798