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The Structure of Models of Peano Arithmetic
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The Structure of Models of Peano Arithmetic

Roman Kossak and James Schmerl

Abstract

This book gives an account of the present state of research on lattices of elementary substructures and automorphisms of nonstandard models of arithmetic. Major representation theorems are proved, and the important particular case of countable recursively saturated models is discussed in detail. All necessary technical tools are developed. The list includes: constructions of elementary simple extensions; a partial classification of arithmetic types, in particular Gaifman's theory of definable types; forcing in arithmetic; elements of the Kirby-Paris combinatorial theory of cuts; Lascar's gener ... More

Keywords: nonstandard models, countable recursively saturated models, Gaifman's theory, Kirby-Paris, Lascar's generic automorphisms, Ramsey's theorem

Bibliographic Information

Print publication date: 2006 Print ISBN-13: 9780198568278
Published to Oxford Scholarship Online: September 2007 DOI:10.1093/acprof:oso/9780198568278.001.0001

Authors

Affiliations are at time of print publication.

Roman Kossak, author
City University of New York

James Schmerl, author
University of Connecticut, Storrs

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