Nonstandard second-order arithmetic and Riemann's mapping theorem

Yoshihiro Horihata, Keita Yokoyama

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)520-551
Number of pages32
JournalAnnals of Pure and Applied Logic
Volume165
Issue number2
DOIs
Publication statusPublished - 2014 Feb

Keywords

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

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