Notre Dame Journal of Formal Logic

Arithmetically Saturated Models of Arithmetic

Roman Kossak and James H. Schmerl


The paper presents an outline of the general theory of countable arithmetically saturated models of PA and some of its applications. We consider questions concerning the automorphism group of a countable recursively saturated model of PA. We prove new results concerning fixed point sets, open subgroups, and the cofinality of the automorphism group. We also prove that the standard system of a countable arithmetically saturated model of PA is determined by the lattice of its elementary substructures.

Article information

Notre Dame J. Formal Logic, Volume 36, Number 4 (1995), 531-546.

First available in Project Euclid: 17 December 2002

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Zentralblatt MATH identifier

Primary: 03C62: Models of arithmetic and set theory [See also 03Hxx]
Secondary: 03C57: Effective and recursion-theoretic model theory [See also 03D45]


Kossak, Roman; Schmerl, James H. Arithmetically Saturated Models of Arithmetic. Notre Dame J. Formal Logic 36 (1995), no. 4, 531--546. doi:10.1305/ndjfl/1040136914.

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