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The Structure of Models of Peano Arithmetic$
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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

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HOW TO CONTROL TYPES

HOW TO CONTROL TYPES

Chapter:
(p.135) 5 HOW TO CONTROL TYPES
Source:
The Structure of Models of Peano Arithmetic
Author(s):

Roman Kossak

James H. Schmerl

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198568278.003.0005

This chapter makes use of an induced version of Ramsey's Theorem to prove several results: the Abramson-Harrington theorem on omitting large indiscernible sets and Hanf numbers for models of arithmetic; a theorem characterizing the possible automorphism groups of models; and a theorem based on countable recursively saturated models being generated by a set of indiscernibles.

Keywords:   Ramsey's Theorem, Abramson-Harrington theorem, Hanf numbers, automorphism groups, indiscernibles

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