Nonstandard second-order arithmetic and Riemann's mapping theorem

Yoshihiro Horihata; Keita Yokoyama

doi:10.1016/j.apal.2013.06.022

Nonstandard second-order arithmetic and Riemann's mapping theorem

Yoshihiro Horihata, Keita Yokoyama

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 Riemann's mapping theorem, and show several different versions of Riemann's mapping theorem.

Original language	English
Pages (from-to)	520-551
Number of pages	32
Journal	Annals of Pure and Applied Logic
Volume	165
Issue number	2
DOIs	https://doi.org/10.1016/j.apal.2013.06.022
Publication status	Published - 2014 Feb
Externally published	Yes

Keywords

Nonstandard analysis
Reverse mathematics
Riemann's mapping theorem
Second-order arithmetic

ASJC Scopus subject areas

Logic

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10.1016/j.apal.2013.06.022

Cite this

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AU - Yokoyama, Keita

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AB - 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 Riemann's mapping theorem, and show several different versions of Riemann's mapping theorem.

KW - Nonstandard analysis

KW - Reverse mathematics

KW - Riemann's mapping theorem

KW - Second-order arithmetic

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Nonstandard second-order arithmetic and Riemann's mapping theorem

Abstract

Keywords

ASJC Scopus subject areas

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