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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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The Structure of Models of Peano Arithmetic

Roman Kossak

James H. Schmerl

Oxford University Press

This chapter introduces some techniques for constructing elementary simple extensions. In particular, it includes proof of the existence of superminimal elementary end extensions of countable models and a construction of a Jónsson model. The MacDowell-Specker Theorem is proved and some of its consequences derived, including results on conservative extensions, rather classless models and amalgamations. The chapter concludes with a discussion of nonelementary extensions and the theorem of Wilkie on end extensions which are not σ1-elementary.

Keywords:   simple extensions, elementary extensions, minimal extensions, MacDowell-Specker Theorem, conservative extensions, amalgamations

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