Nonstandard arithmetic and reverse mathematics

Bulletin of Symbolic Logic 12 (1):100-125 (2006)
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
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DOI 10.2178/bsl/1140640945
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References found in this work BETA
The Self-Embedding Theorem of WKL< Sub> 0 and a Non-Standard Method.Kazuyuki Tanaka - 1997 - Annals of Pure and Applied Logic 84 (1):41-49.
On the Strength of Nonstandard Analysis.C. Ward Henson & H. Jerome Keisler - 1986 - Journal of Symbolic Logic 51 (2):377-386.

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Citations of this work BETA
Erna and Friedman's Reverse Mathematics.Sam Sanders - 2011 - Journal of Symbolic Logic 76 (2):637 - 664.
Nonstandard Arithmetic and Recursive Comprehension.H. Jerome Keisler - 2010 - Annals of Pure and Applied Logic 161 (8):1047-1062.
Formalizing Non-Standard Arguments in Second-Order Arithmetic.Keita Yokoyama - 2010 - Journal of Symbolic Logic 75 (4):1199-1210.
Relative Arithmetic.Sam Sanders - 2010 - Mathematical Logic Quarterly 56 (6):564-572.

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