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Full Description
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 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.
Contents
Non-standard models in a broader perspective by H. Gaifman Coding in $I\Delta_0$ by P. D'Aquino and J. F. Knight Automorphisms, Mahlo cardinals, and NFU by A. Enayat AC fails in the natural analogues of V and L that model the stratified fragment of ZF by T. Forster Working with nonstandard models by H. M. Friedman Internally iterated ultrapowers by K. Hrbacek On some questions of Hrbacek and Di Nasso by R. Jin Turing upper bounds of jump ideals and Scott sets by A. M. McAllister Diversity in substructures by J. H. Schmerl Automorphisms of countable recursively saturated models of set theory by A. A. Togha.
