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
Chapter 1: An Introduction to Proof Theory & Chapter 2: Firstorder Proof Theory of Arithmetic.S. Buss - 1998 - In Samuel R. Buss (ed.), Handbook of Proof Theory. Elsevier.
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.
View all 7 references / Add more references
Citations of this work BETA
Ultrafilters in Reverse Mathematics.Henry Towsner - 2014 - Journal of Mathematical Logic 14 (1):1450001.
Nonstandard Second-Order Arithmetic and Riemannʼs Mapping Theorem.Yoshihiro Horihata & Keita Yokoyama - 2014 - Annals of Pure and Applied Logic 165 (2):520-551.
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