Items related to Models of Peano Arithmetic (Oxford Logic Guides)
Synopsis
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.
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About the Author
Richard Kaye, Junior Research Fellow, Jesus College, Oxford.
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Models of Peano Arithmetic (Hardcover)
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Oxford University Press, Oxford, 1991
ISBN 10: 019853213X
ISBN 13: 9780198532132
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Hardcover. Condition: new. Hardcover. Nonstandard models of arithmetic are of interest to mathematicians through the presence of infinite (or nonstandard) integers and the various properties they inherit from the finite integers. Since their introduction in the 1930s (by Skolem and Goedel ), 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 stressesthe interplay between the first-order theory, recursion-theoretic aspects, and the structural properties of these models. Prerequisites have been kept to a minimum. A basic groundingin elementary model theory and a familiarity with the notions of recursive, primitive recursive, and r.e. sets will be sufficient. Consequently, the book should be suitable for postgraduate students coming to the subject for the first time and a variety of exercises of varying degrees of difficulty will help to further the reader's understanding. Beginning with Goedel's incompleteness theorem, the book covers the prime models, cofinal extensions, end extensions,Gaifman's construction of a definable type, Tennenbaum's theorem, Friedman's theorem and subsequent work on indicators, and culminates in a chapter on recursive saturation and resplendency. An introduction to the developments of nonstandard models. Beginning with Godel's incompleteness theorem, it covers the prime models, cofinal extensions, and extensions, Gaifman's construction of a definable type, Tennenbaum's theorem and Friedman's theorem on indicators, ending with a chapter on recursive saturation and resplendency. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Seller Inventory # 9780198532132
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Models of Peano Arithmetic
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