Nonstandard Models of Arithmetic and Set Theory: AMS Special Session Nonstandard Models of Arithmetic and Set Theory, January 15-16, 2003, Baltimore, Maryland

Przednia okładka
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.
 

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Spis treści

NonStandard Models in a Broader Perspective
1
Coding in IΔ0
23
Automorphisms Mahlo Cardinals and NFU
37
AC Fails in the Natural Analogues of V and L that Model the Stratified Fragment of ZF
61
Working with Nonstandard Models
71
Internally Iterated Ultrapowers
87
On Some Questions of Hrbacek and Di Nasso
121
Turing Upper Bounds of Jump Ideals and Scott Sets
129
Diversity in Substructures
145
Automorphisms of Countable Recursively Saturated Models of Set Theory
163
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