Nonstandard models in recursion theory and reverse mathematics

Bulletin of Symbolic Logic 20 (2):170-200 (2014)

Chaehyun Chong
Sogang University
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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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.David Seetapun & Theodore A. Slaman - 1995 - Notre Dame Journal of Formal Logic 36 (4):570-582.

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