Formalizing non-standard arguments in second-order arithmetic

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

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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DOI 10.2178/jsl/1286198143
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References found in this work BETA

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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Ultrafilters in Reverse Mathematics.Henry Towsner - 2014 - Journal of Mathematical Logic 14 (1):1450001.

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