Bulletin of Symbolic Logic

Nonstandard arithmetic and reverse mathematics

H. Jerome Keisler

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Abstract

We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [3] we introduced saturation principles in nonstandard arithmetic which are equivalent in strength to strong choice axioms in second order arithmetic. This paper studies principles which are equivalent in strength to weaker theories in second order arithmetic.

Article information

Source
Bull. Symbolic Logic, Volume 12, Issue 1 (2006), 100-125.

Dates
First available in Project Euclid: 22 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1140640945

Digital Object Identifier
doi:10.2178/bsl/1140640945

Mathematical Reviews number (MathSciNet)
MR2209331

Zentralblatt MATH identifier
1101.03040

Citation

Keisler, H. Jerome. Nonstandard arithmetic and reverse mathematics. Bull. Symbolic Logic 12 (2006), no. 1, 100--125. doi:10.2178/bsl/1140640945. https://projecteuclid.org/euclid.bsl/1140640945


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