Jump to ContentJump to Main Navigation
The Structure of Models of Peano Arithmetic$
Users without a subscription are not able to see the full content.

Roman Kossak and James Schmerl

Print publication date: 2006

Print ISBN-13: 9780198568278

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198568278.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 15 November 2019

AUTOMORPHISM GROUPS OF RECURSIVELY SATURATED MODELS

AUTOMORPHISM GROUPS OF RECURSIVELY SATURATED MODELS

Chapter:
(p.230) 9 AUTOMORPHISM GROUPS OF RECURSIVELY SATURATED MODELS
Source:
The Structure of Models of Peano Arithmetic
Author(s):

Roman Kossak

James H. Schmerl

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198568278.003.0009

This chapter shows two major results. One, due to Lascar, says that countable arithmetically saturated models of PA have sequences of generic automorphisms, and consequently have a small index property. The other, from the authors of the book, states that the standard systems of countable arithmetically saturated models of PA are coded in their automorphism groups. Other results shown include proving a connection between the existence of automorphims with dense conjugacy classes and providing answers to some combinatorial questions concerning coloring of Cartesian products of digraphs; and a theorem saying that the cofinality of the automorphism group of a countable recursively saturated model of PA is uncountable if and only if the model is arithmetically saturated.

Keywords:   Lascar, saturated models of PA, automorphims, Cartesian products of digraphs

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .