Nonstandard models in recursion theory and reverse mathematics
Bulletin of Symbolic Logic 20 (2):170-200 (2014)
| Authors |
Chaehyun Chong
Sogang University
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| Abstract |
We give a survey of the study of nonstandard models in recursion theory and reverse mathematics. We discuss the key notions and techniques in effective computability in nonstandard models, and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic. Particular attention is given to principles related to Ramsey’s Theorem for Pairs.
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| DOI | 10.1017/bsl.2014.14 |
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References found in this work BETA
The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Pure and Applied Logic 4 (3):229.
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.
Combinatorial Principles Weaker Than Ramsey's Theorem for Pairs.Denis R. Hirschfeldt & Richard A. Shore - 2007 - Journal of Symbolic Logic 72 (1):171-206.
Separating Principles Below Ramsey's Theorem for Pairs.Manuel Lerman, Reed Solomon & Henry Towsner - 2013 - Journal of Mathematical Logic 13 (2):1350007.
On the Strength of Ramsey's Theorem.David Seetapun & Theodore A. Slaman - 1995 - Notre Dame Journal of Formal Logic 36 (4):570-582.
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Citations of this work BETA
Comparing the Strength of Diagonally Nonrecursive Functions in the Absence of Induction.François G. Dorais, Jeffry L. Hirst & Paul Shafer - 2015 - Journal of Symbolic Logic 80 (4):1211-1235.
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