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 WKL₀DOI
10.2178/jsl/1286198143
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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.
Nonstandard second-order arithmetic and Riemannʼs mapping theorem.Yoshihiro Horihata & Keita Yokoyama - 2014 - Annals of Pure and Applied Logic 165 (2):520-551.
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.
References found in this work
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.
