Notre Dame Journal of Formal Logic 49 (4):345-360 (2008)

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 recursively saturated model of which can be extended to an automorphism of the countable recursively saturated elementary end extension of the model
Keywords short recursive saturation   recursive saturation   models of PA   automorphisms
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DOI 10.1215/00294527-2008-016
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Models and Types of Peano's Arithmetic.Haim Gaifman - 1976 - Annals of Mathematical Logic 9 (3):223-306.
Recursively Saturated Nonstandard Models of Arithmetic.C. Smoryński - 1981 - Journal of Symbolic Logic 46 (2):259-286.
Discernible Elements in Models for Peano Arithmetic.Andrzej Ehrenfeucht - 1973 - Journal of Symbolic Logic 38 (2):291-292.

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