The Structure of Models of Peano Arithmetic

Hardcover | July 29, 2006

byRoman Kossak, James Schmerl

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Aimed at graduate students and research logicians and mathematicians, this much-awaited text covers over forty years of work on relative classification theory for non-standard models of arithmetic. With graded exercises at the end of each chapter, the book covers basic isomorphism invariants:families of types realized in a model, lattices of elementary substructures and automorphism groups. Many results involve applications of the powerful technique of minimal types due to Haim Gaifman, and some of the results are classical but have never been published in a book form before.

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From the Publisher

Aimed at graduate students and research logicians and mathematicians, this much-awaited text covers over forty years of work on relative classification theory for non-standard models of arithmetic. With graded exercises at the end of each chapter, the book covers basic isomorphism invariants:families of types realized in a model, latt...

Roman Kossak is with the City University of New York. James Schmerl is with the University of Connecticut, Storrs.
Format:HardcoverDimensions:328 pages, 9.21 × 6.14 × 0.87 inPublished:July 29, 2006Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198568274

ISBN - 13:9780198568278

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Extra Content

Table of Contents

Preface1. Basics2. Extensions3. Minimal and other types4. Substructure lattices5. How to control types6. Generics and forcing7. Cuts8. Automorphisms of recursively saturated models9. Automorphism groups of recursively saturated models10. Omega 1-like models11. Order types12. Twenty questionsReferencesIndex

Editorial Reviews

"Taking everything into account, this book is a skillfully written research monograph dedicated to results concerning models of Peano arthmetic, especially ones obtains in the last twenty years or so, and can be recommended without hesitation to anyone wishing to acquire a sound knowledge of the subject."--
athematical Reviews