Bulletin of Symbolic Logic 16 (3):378-402 (2010)
| 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
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| DOI | 10.2178/bsl/1286284559 |
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References found in this work BETA
On the Strength of Ramsey's Theorem for Pairs.Peter A. Cholak, Carl G. Jockusch & Theodore A. Slaman - 2001 - Journal of Symbolic Logic 66 (1):1-55.
Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
Combinatorial Principles Weaker Than Ramsey's Theorem for Pairs.Denis R. Hirschfeldt & Richard A. Shore - 2007 - Journal of Symbolic Logic 72 (1):171-206.
View all 37 references / Add more references
Citations of this work BETA
Set Existence Principles and Closure Conditions: Unravelling the Standard View of Reverse Mathematics.Benedict Eastaugh - 2019 - Philosophia Mathematica 27 (2):153-176.
The Prehistory of the Subsystems of Second-Order Arithmetic.Walter Dean & Sean Walsh - 2017 - Review of Symbolic Logic 10 (2):357-396.
Term Extraction and Ramsey's Theorem for Pairs.Alexander P. Kreuzer & Ulrich Kohlenbach - 2012 - Journal of Symbolic Logic 77 (3):853-895.
Hilbert, Completeness and Geometry.Giorgio Venturi - 2011 - Rivista Italiana di Filosofia Analitica Junior 2 (2):80-102.
On Notions of Computability-Theoretic Reduction Between Π21 Principles.Denis R. Hirschfeldt & Carl G. Jockusch - 2016 - Journal of Mathematical Logic 16 (1):1650002.
View all 7 citations / Add more citations
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