On maximal subgroups of the automorphism group of a countable recursively saturated model of PA

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Annals of Pure and Applied Logic 65 (2):125-148 (1993)
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Abstract

We show that the stabilizer of an element a of a countable recursively saturated model of arithmetic M is a maximal subgroup of Aut iff the type of a is selective. This is a point of departure for a more detailed study of the relationship between pointwise and setwise stabilizers of certain subsets of M and the types of elements in those subsets. We also show that a complete type of PA is 2-indiscernible iff it is minimal in the sense of Gaifman

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10.1016/0168-0072(93)90035-c

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Roman Kossak
City University of New York

Citations of this work

Arithmetically Saturated Models of Arithmetic.Roman Kossak & James H. Schmerl - 1995 - Notre Dame Journal of Formal Logic 36 (4):531-546.
On Cofinal Submodels and Elementary Interstices.Roman Kossak & James H. Schmerl - 2012 - Notre Dame Journal of Formal Logic 53 (3):267-287.
Four Problems Concerning Recursively Saturated Models of Arithmetic.Roman Kossak - 1995 - Notre Dame Journal of Formal Logic 36 (4):519-530.

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References found in this work

Models and types of Peano's arithmetic.Haim Gaifman - 1976 - Annals of Mathematical Logic 9 (3):223-306.
Ultrafilters and types on models of arithmetic.L. A. S. Kirby - 1984 - Annals of Pure and Applied Logic 27 (3):215-252.

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