Book

The Structure of Models of Peano Arithmetic

Roman Kossak and James Schmerl

Published in print June 2006 | ISBN: 9780198568278
Published online September 2007 | e-ISBN: 9780191718199 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780198568278.001.0001

Series: Oxford Logic Guides

The Structure of Models of Peano Arithmetic

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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 generic automorphisms; and applications of Abramson and Harrington's generalization of Ramsey's theorem. There are also chapters discussing ω1-like models with interesting second order properties, and a chapter on order types of nonstandard models.

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

Book.  328 pages.  Illustrated.

Subjects: Logic

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Table of Contents

BASICS in The Structure of Models of Peano Arithmetic

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EXTENSIONS in The Structure of Models of Peano Arithmetic

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MINIMAL AND OTHER TYPES in The Structure of Models of Peano Arithmetic

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SUBSTRUCTURE LATTICES in The Structure of Models of Peano Arithmetic

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HOW TO CONTROL TYPES in The Structure of Models of Peano Arithmetic

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GENERICS AND FORCING in The Structure of Models of Peano Arithmetic

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CUTS in The Structure of Models of Peano Arithmetic

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AUTOMORPHISMS OF RECURSIVELY SATURATED MODELS in The Structure of Models of Peano Arithmetic

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AUTOMORPHISM GROUPS OF RECURSIVELY SATURATED MODELS in The Structure of Models of Peano Arithmetic

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ω<sub>1</sub>-LIKE MODELS in The Structure of Models of Peano Arithmetic

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