Formalizing non-standard arguments in second-order arithmetic

Journal of Symbolic Logic 75 (4):1199-1210 (2010)
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Abstract

In this paper, we introduce the systems ns-ACA₀ and ns-WKL₀ of non-standard second-order arithmetic in which we can formalize non-standard arguments in ACA₀ and WKL₀, respectively. Then, we give direct transformations from non-standard proofs in ns-ACA₀ or ns-WKL₀ into proofs in ACA₀ or WKL₀

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Citations of this work

A Nonstandard Counterpart of WWKL.Stephen G. Simpson & Keita Yokoyama - 2011 - Notre Dame Journal of Formal Logic 52 (3):229-243.
Ultrafilters in reverse mathematics.Henry Towsner - 2014 - Journal of Mathematical Logic 14 (1):1450001.
Nonstandard arithmetic and recursive comprehension.H. Jerome Keisler - 2010 - Annals of Pure and Applied Logic 161 (8):1047-1062.

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References found in this work

Formalizing forcing arguments in subsystems of second-order arithmetic.Jeremy Avigad - 1996 - Annals of Pure and Applied Logic 82 (2):165-191.
Nonstandard arithmetic and reverse mathematics.H. Jerome Keisler - 2006 - Bulletin of Symbolic Logic 12 (1):100-125.
The self-embedding theorem of WKL0 and a non-standard method.Kazuyuki Tanaka - 1997 - Annals of Pure and Applied Logic 84 (1):41-49.
Non‐standard Analysis in WKL0.Kazuyuki Tanaka - 1997 - Mathematical Logic Quarterly 43 (3):396-400.

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