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Nonstandard Models of Arithmetic and Set Theory
Edited by: Ali Enayat, American University, Washington, DC, and Roman Kossak, City University of New York, NY

Contemporary Mathematics
2004; 167 pp; softcover
Volume: 361
ISBN-10: 0-8218-3535-1
ISBN-13: 978-0-8218-3535-7
List Price: US$65
Member Price: US$52
Order Code: CONM/361
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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 non-standardness 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 non-Euclidean 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.


Graduate students and research mathematicians interested in logic, especially model theory.

Table of Contents

  • H. Gaifman -- Non-standard 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
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