A Galois correspondence for countable short recursively saturated models of PA

Mathematical Logic Quarterly 56 (3):228-238 (2010)
  Copy   BIBTEX

Abstract

In this paper we investigate the properties of automorphism groups of countable short recursively saturated models of arithmetic. In particular, we show that Kaye's Theorem concerning the closed normal subgroups of automorphism groups of countable recursively saturated models of arithmetic applies to automorphism groups of countable short recursively saturated models as well. That is, the closed normal subgroups of the automorphism group of a countable short recursively saturated model of PA are exactly the stabilizers of the invariant cuts of the model which are closed under exponentiation. This Galois correspondence is used to show that there are countable short recursively saturated models of arithmetic whose automorphism groups are not isomorphic as topological groups. Moreover, we show that the automorphism groups of countable short arithmetically saturated models of PA are not topologically isomorphic to the automorphism groups of countable short recursively saturated models of PA which are not short arithmetically saturated

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 94,420

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Automorphisms of Countable Short Recursively Saturated Models of PA.Erez Shochat - 2008 - Notre Dame Journal of Formal Logic 49 (4):345-360.
Arithmetically Saturated Models of Arithmetic.Roman Kossak & James H. Schmerl - 1995 - Notre Dame Journal of Formal Logic 36 (4):531-546.
Automorphism Groups of Arithmetically Saturated Models.Ermek S. Nurkhaidarov - 2006 - Journal of Symbolic Logic 71 (1):203 - 216.

Analytics

Added to PP
2013-12-01

Downloads
18 (#842,756)

6 months
8 (#525,169)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations