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)
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| Keywords | Riemann mapping theorem non‐standard analysis Reverse mathematics |
| Categories | (categorize this paper) |
| DOI | 10.1002/malq.200610033 |
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References found in this work BETA
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.
Citations of this work BETA
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.
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