Arithmetically saturated models of arithmetic. (English) Zbl 0848.03017

Kossak, Roman; Schmerl, James H.

Notre Dame J. Formal Logic 36, No. 4, 531-546 (1995).

A model of a first-order theory is arithmetically saturated if it is saturated with respect to the types that are arithmetic in the complete types realized in the model. The paper presents an outline of the general theory of countable arithmetically saturated models of PA and some of its applications. The results concern the automorphism group of a countable recursively saturated model of PA. New results on fixed point sets, open subgroups, and the cofinality of the automorphisms group are given. It is also shown that the standard system of a countable arithmetically saturated model of PA is determined by the lattice of the elementary substructures of the model.

Reviewer: R.Kossak (New York)

MSC:

03C62	Models of arithmetic and set theory
03C50	Models with special properties (saturated, rigid, etc.)

Keywords:

Peano arithmetic; recursive saturation; lattice of elementary substructures; arithmetically saturated models of PA; automorphism group; fixed point; open subgroups; cofinality

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