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Reverse Mathematics: The Playground of Logic

Published online by Cambridge University Press:  15 January 2014

Richard A. Shore
Richard A. Shore*
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA, E-mail: [email protected]
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Abstract

This paper is essentially the author's Gödel Lecture at the ASL Logic Colloquium '09 in Sofia extended and supplemented by material from some other papers. After a brief description of traditional reverse mathematics, a computational approach to is presented. There are then discussions of some interactions between reverse mathematics and the major branches of mathematical logic in terms of the techniques they supply as well as theorems for analysis. The emphasis here is on ones that lie outside the usual main systems of reverse mathematics. While retaining the usual base theory and working still within second order arithmetic, theorems are described that range from those far below the usual systems to ones far above.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 16 , Issue 3 , September 2010 , pp. 378 - 402
Copyright
Copyright © Association for Symbolic Logic 2010

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