Annals of Pure and Applied Logic 55 (1):67-99 (1991)

Authors
Roman Kossak
City University of New York
Abstract
We give an examination of the automorphism group Aut of a countable recursively saturated model M of PA. The main result is a characterisation of strong elementary initial segments of M as the initial segments consisting of fixed points of automorphisms of M. As a corollary we prove that, for any consistent completion T of PA, there are recursively saturated countable models M1, M2 of T, such that Aut[ncong]Aut, as topological groups with a natural topology. Other results include a classification of the normal subgroups of Aut of the form [lcub]g: g [uharr] A = idA[rcub], for sets A M, and a highly homogeneous representation of Aut as a subgroup of Aut
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/0168-0072(91)90098-7
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 63,323
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Models and Types of Peano's Arithmetic.Haim Gaifman - 1976 - Annals of Mathematical Logic 9 (3):223-306.
Models of Peano Arithmetic.Richard Kaye - 1991 - Clarendon Press.
Toward Model Theory Through Recursive Saturation.John Stewart Schlipf - 1978 - Journal of Symbolic Logic 43 (2):183-206.
Recursively Saturated Nonstandard Models of Arithmetic.C. Smoryński - 1981 - Journal of Symbolic Logic 46 (2):259-286.

View all 15 references / Add more references

Citations of this work BETA

Fixed Points of Self-Embeddings of Models of Arithmetic.Saeideh Bahrami & Ali Enayat - 2018 - Annals of Pure and Applied Logic 169 (6):487-513.
Iterated Ultrapowers for the Masses.Ali Enayat, Matt Kaufmann & Zachiri McKenzie - 2018 - Archive for Mathematical Logic 57 (5-6):557-576.
Automorphisms of Models of Arithmetic: A Unified View.Ali Enayat - 2007 - Annals of Pure and Applied Logic 145 (1):16-36.
Arithmetically Saturated Models of Arithmetic.Roman Kossak & James H. Schmerl - 1995 - Notre Dame Journal of Formal Logic 36 (4):531-546.

View all 27 citations / Add more citations

Similar books and articles

Four Problems Concerning Recursively Saturated Models of Arithmetic.Roman Kossak - 1995 - Notre Dame Journal of Formal Logic 36 (4):519-530.
Automorphisms of Countable Short Recursively Saturated Models of PA.Erez Shochat - 2008 - Notre Dame Journal of Formal Logic 49 (4):345-360.
Automorphisms of Countable Recursively Saturated Models of PA: A Survey.Henryk Kotlarski - 1995 - Notre Dame Journal of Formal Logic 36 (4):505-518.
The Recursively Saturated Part of Models of Peano Arithmetic.Henryk Kotlarski - 1986 - Mathematical Logic Quarterly 32 (19‐24):365-370.
The Ω-Like Recursively Saturated Models of Arithmetic.Roman Kossak - 1991 - Bulletin of the Section of Logic 20 (3/4):109-109.
Recursively Saturated $\omega_1$-Like Models of Arithmetic.Roman Kossak - 1985 - Notre Dame Journal of Formal Logic 26 (4):413-422.
Models with the Ω-Property.Roman Kossak - 1989 - Journal of Symbolic Logic 54 (1):177-189.
Arithmetically Saturated Models of Arithmetic.Roman Kossak & James H. Schmerl - 1995 - Notre Dame Journal of Formal Logic 36 (4):531-546.

Analytics

Added to PP index
2014-01-16

Total views
8 ( #977,558 of 2,448,710 )

Recent downloads (6 months)
4 ( #178,140 of 2,448,710 )

How can I increase my downloads?

Downloads

My notes