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On maximal subgroups of the automorphism group of a countable recursively saturated model of PA
Annals of Pure and Applied Logic 65 (2):125-148 (1993)
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 GaifmanAuthor's Profile
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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 two questions concerning the automorphism groups of countable recursively saturated models of PA.Roman Kossak & Nicholas Bamber - 1996 - Archive for Mathematical Logic 36 (1):73-79.
On Cofinal Submodels and Elementary Interstices.Roman Kossak & James H. Schmerl - 2012 - Notre Dame Journal of Formal Logic 53 (3):267-287.
Automorphisms of Saturated and Boundedly Saturated Models of Arithmetic.Ermek S. Nurkhaidarov & Erez Shochat - 2011 - Notre Dame Journal of Formal Logic 52 (3):315-329.
Automorphisms of Models of True Arithmetic: Recognizing Some Basic Open Subgroups.Henryk Kotlarski & Richard Kaye - 1994 - Notre Dame Journal of Formal Logic 35 (1):1-14.
References found in this work
Models and types of Peano's arithmetic.Haim Gaifman - 1976 - Annals of Mathematical Logic 9 (3):223-306.
Automorphisms of recursively saturated models of arithmetic.Richard Kaye, Roman Kossak & Henryk Kotlarski - 1991 - Annals of Pure and Applied Logic 55 (1):67-99.
Ultrafilters and types on models of arithmetic.L. A. S. Kirby - 1984 - Annals of Pure and Applied Logic 27 (3):215-252.
A note on initial segment constructions in recursively saturated models of arithmetic.C. Smoryński - 1982 - Notre Dame Journal of Formal Logic 23 (4):393-408.
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