Non-standard analysis in ACA0 and Riemann mapping theorem
Mathematical Logic Quarterly 53 (2):132-146 (2007)
Abstract
This research is motivated by the program of reverse mathematics and non-standard arguments in second-order arithmetic. Within a weak subsystem of second-order arithmetic ACA0, we investigate some aspects of non-standard analysis related to sequential compactness. Then, using arguments of non-standard analysis, we show the equivalence of the Riemann mapping theorem and ACA0 over WKL0. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)DOI
10.1002/malq.200610033
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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.
Formalizing non-standard arguments in second-order arithmetic.Keita Yokoyama - 2010 - Journal of Symbolic Logic 75 (4):1199-1210.
Nonstandard second-order arithmetic and Riemannʼs mapping theorem.Yoshihiro Horihata & Keita Yokoyama - 2014 - Annals of Pure and Applied Logic 165 (2):520-551.
10th Asian Logic Conference: Sponsored by the Association for Symbolic Logic.Toshiyasu Arai - 2009 - Bulletin of Symbolic Logic 15 (2):246-265.
References found in this work
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.
