Nonstandard arithmetic and reverse mathematics

Bulletin of Symbolic Logic 12 (1):100-125 (2006)
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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

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10.2178/bsl/1140640945

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Citations of this work

Reverse mathematics: the playground of logic.Richard A. Shore - 2010 - Bulletin of Symbolic Logic 16 (3):378-402.
A Nonstandard Counterpart of WWKL.Stephen G. Simpson & Keita Yokoyama - 2011 - Notre Dame Journal of Formal Logic 52 (3):229-243.
Infinitesimal analysis without the Axiom of Choice.Karel Hrbacek & Mikhail G. Katz - 2021 - Annals of Pure and Applied Logic 172 (6):102959.
Erna and Friedman's reverse mathematics.Sam Sanders - 2011 - Journal of Symbolic Logic 76 (2):637 - 664.

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References found in this work

Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
On the strength of nonstandard analysis.C. Ward Henson & H. Jerome Keisler - 1986 - Journal of Symbolic Logic 51 (2):377-386.
The self-embedding theorem of WKL0 and a non-standard method.Kazuyuki Tanaka - 1997 - Annals of Pure and Applied Logic 84 (1):41-49.

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