Models of Peano Arithmetic

Models of Peano Arithmetic

by Richard Kaye

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Overview

Non-standard models of arithmetic are of interest to mathematicians through the presence of infinite integers and the various properties they inherit from the finite integers. Since their introduction in the 1930s, they have come to play an important role in model theory, and in combinatorics through independence results such as the Paris-Harrington theorem. This book is an introduction to these developments, and stresses the interplay between the first-order theory, recursion-theoretic aspects, and the structural properties of these models. Prerequisites for an understanding of the text have been kept to a minimum, these being a basic grounding in elementary model theory and a familiarity with the notions of recursive, primitive recursive, and r.e. sets. Consequently, the book is suitable for postgraduate students coming to the subject for the first time, and a number of exercises of varying degrees of difficulty will help to further the reader's understanding.

Product Details

ISBN-13: 9780198532132
Publisher: Oxford University Press, USA
Publication date: 02/28/1991
Series: Oxford Logic Guides Series , #15
Pages: 304
Product dimensions: 6.38(w) x 9.50(h) x 0.88(d)

About the Author

Jesus College, Oxford

Table of Contents

1. The Standard Model
2. Discretely Ordered Rings
3. Gödel Incompleteness
4. The Axioms of Peano Arithmetic
5. Some Number Theory in Peano Arithmetic
6. Models of Peano Arithmetic
7. Collection
8. Prime Models
9. Satisfaction
10. Subsystems of Peano Arithmetic
11. Saturation
12. Initial Segments
13. The Standard System
14. Indicators
15. Recursive Saturation
16. Suggestions for Further Reading

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