Contemporary Mathematics 2004; 167 pp; softcover Volume: 361 ISBN10: 0821835351 ISBN13: 9780821835357 List Price: US$65 Member Price: US$52 Order Code: CONM/361
 This is the proceedings of the AMS special session on nonstandard models of arithmetic and set theory held at the Joint Mathematics Meetings in Baltimore (MD). The volume opens with an essay from Haim Gaifman that probes the concept of nonstandardness in mathematics and provides a fascinating mix of historical and philosophical insights into the nature of nonstandard mathematical structures. In particular, Gaifman compares and contrasts the discovery of nonstandard models with other key mathematical innovations, such as the introduction of various number systems, the modern concept of function, and nonEuclidean geometries. Other articles in the book present results related to nonstandard models in arithmetic and set theory, including a survey of known results on the Turing upper bounds of arithmetic sets and functions. The volume is suitable for graduate students and research mathematicians interested in logic, especially model theory. Readership Graduate students and research mathematicians interested in logic, especially model theory. Table of Contents  H. Gaifman  Nonstandard models in a broader perspective
 P. D'Aquino and J. F. Knight  Coding in \(I\Delta_0\)
 A. Enayat  Automorphisms, Mahlo cardinals, and NFU
 T. Forster  AC fails in the natural analogues of V and L that model the stratified fragment of ZF
 H. M. Friedman  Working with nonstandard models
 K. Hrbacek  Internally iterated ultrapowers
 R. Jin  On some questions of Hrbacek and Di Nasso
 A. M. McAllister  Turing upper bounds of jump ideals and Scott sets
 J. H. Schmerl  Diversity in substructures
 A. A. Togha  Automorphisms of countable recursively saturated models of set theory
