Bulletin of Symbolic Logic 20 (2):170-200 (2014)
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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
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.
On the Strength of Ramsey's Theorem.David Seetapun & Theodore A. Slaman - 1995 - Notre Dame Journal of Formal Logic 36 (4):570-582.
The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Ramsey's Theorem and Recursion Theory.Carl G. Jockusch - 1972 - Journal of Symbolic Logic 37 (2):268-280.
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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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