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NONSTANDARD MODELS IN RECURSION THEORY AND REVERSE MATHEMATICS

Published online by Cambridge University Press:  26 June 2014

C. T. CHONG,
WEI LI and
YUE YANG
C. T. CHONG
Affiliation:
DEPARTMENT OF MATHEMATICS NATIONAL UNIVERSITY OF SINGAPORE 10 LOWER KENT RIDGE ROAD SINGAPORE 119076, SINGAPORE
WEI LI*
Affiliation:
DEPARTMENT OF MATHEMATICS NATIONAL UNIVERSITY OF SINGAPORE 10 LOWER KENT RIDGE ROAD SINGAPORE 119076, SINGAPORE
YUE YANG
Affiliation:
DEPARTMENT OF MATHEMATICS NATIONAL UNIVERSITY OF SINGAPORE 10 LOWER KENT RIDGE ROAD SINGAPORE 119076, SINGAPORE
*
*Current address of Wei Li: KURT GÖDEL RESEARCH CENTER FOR MATHEMATICAL LOGIC UNIVERSITY OF VIENNA, AUSTRIA E-mail:chongct@math.nus.edu.sgE-mail:wei.li@univie.ac.atE-mail:matyangy@nus.edu.sg
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Abstract

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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.

Keywords

Nonstandard modelsfragments of Peano arithmeticreverse mathematicsreverse recursion theorycombinatorial principlesRamsey’s Theorem for Pairs

Information

Type
Articles
Information
Bulletin of Symbolic Logic , Volume 20 , Issue 2 , June 2014, pp. 170 - 200
Copyright
Copyright © The Association for Symbolic Logic 2014 

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