Nonstandard models in recursion theory and reverse mathematics

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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References found in this work

On the Strength of Ramsey's Theorem.David Seetapun & Theodore A. Slaman - 1995 - Notre Dame Journal of Formal Logic 36 (4):570-582.
Ramsey's theorem and recursion theory.Carl G. Jockusch - 1972 - Journal of Symbolic Logic 37 (2):268-280.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.

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