Models of Peano Arithmetic

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 aspec…