**Contemporary Mathematics**

Volume: 361;
2004;
167 pp;
Softcover

MSC: Primary 03; 26;

**Print ISBN: 978-0-8218-3535-7
Product Code: CONM/361**

List Price: $74.00

AMS Member Price: $59.20

MAA Member Price: $66.60

**Electronic ISBN: 978-0-8218-7951-1
Product Code: CONM/361.E**

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

# Nonstandard Models of Arithmetic and Set Theory

Share this page *Edited by *
*Ali Enayat; Roman Kossak*

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.

#### Readership

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

# Table of Contents

## Nonstandard Models of Arithmetic and Set Theory

- Contents vii8 free
- Preface ix10 free
- Non-Standard Models in a Broader Perspective 114 free
- Coding in IΔ0 2336
- Automorphisms, Mahlo Cardinals, and NFU 3750
- AC Fails in the Natural Analogues of V and L that Model the Stratified Fragment of ZF 6174
- Working with Nonstandard Models 7184
- Internally Iterated Ultrapowers 87100
- On Some Questions of Hrbacek and Di Nasso 121134
- Turing Upper Bounds of Jump Ideals and Scott Sets 129142
- Diversity in Substructures 145158
- Automorphisms of Countable Recursively Saturated Models of Set Theory 163176