Models of Peano Arithmetic (Oxford Logic Guides)

Richard Kaye, "Models of Peano Arithmetic (Oxford Logic Guides)"
Oxford University Press, USA | 1991 | ISBN: 019853213X | 304 pages | PDF | 4,2 MB

Non-vexillum 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 work freely an important role in model theory, and in combinatorics through liberty results such as the Paris-Harrington theorem. This book is each introduction to these developments, and stresses the interplay between the before anything else-order theory, recursion-theoretic aspects, and the structural properties of these models. Prerequisites with regard to an understanding of the text have been kept to a minimum, these being a basic grounding in elementary model theory and a informality with the notions of recursive, primitive recursive, and r.e. sets. Consequently, the part is suitable for postgraduate students coming to the subject for the elementary time, and a number of exercises of varying degrees of hindrance will help to further the reader's understanding.

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