AUTOMORPHISMS OF RECURSIVELY SATURATED MODELS

This chapter develops the basic theory of automorphisms of countable recursively saturated models of PA. The key results are: Smoryìnski's characterization of exponentially closed cuts, the Moving Gaps Lemma, a theorem on extending automorphisms to end extensions, and the characterization of arithmetic saturation in terms of maximal automorphisms. The chapter also includes more results on fixed point sets, various characterizations of arithmetic saturation in terms of the standard topology on the automorphism group, and a theorem on maximal point stabilizers and selective types.

This chapter develops the basic theory of automorphisms of countable recursively saturated models of PA. The key results are: Smoryìnski's characterization of exponentially closed cuts, the Moving Gaps Lemma, a theorem on extending automorphisms to end extensions, and the characterization of arithmetic saturation in terms of maximal automorphisms. The chapter also includes more results on fixed point sets, various characterizations of arithmetic saturation in terms of the standard topology on the automorphism group, and a theorem on maximal point stabilizers and selective types.