Nonstandard second-order arithmetic and Riemannʼs mapping theorem

Annals of Pure and Applied Logic 165 (2):520-551 (2014)

Abstract
In this paper, we introduce systems of nonstandard second-order arithmetic which are conservative extensions of systems of second-order arithmetic. Within these systems, we do reverse mathematics for nonstandard analysis, and we can import techniques of nonstandard analysis into analysis in weak systems of second-order arithmetic. Then, we apply nonstandard techniques to a version of Riemannʼs mapping theorem, and show several different versions of Riemannʼs mapping theorem
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DOI 10.1016/j.apal.2013.06.022
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References found in this work BETA

Measure Theory and Weak König's Lemma.Xiaokang Yu & Stephen G. Simpson - 1990 - Archive for Mathematical Logic 30 (3):171-180.
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.
Erna and Friedman's Reverse Mathematics.Sam Sanders - 2011 - Journal of Symbolic Logic 76 (2):637 - 664.

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