The Jordan curve theorem and the Schönflies theorem in weak second-order arithmetic

DOI10.1007/s00153-007-0050-6zbMath1114.03047OpenAlexW2025876280WikidataQ56020975 ScholiaQ56020975MaRDI QIDQ884957

Keita Yokoyama, Nobuyuki Sakamoto

Publication date: 7 June 2007

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00153-007-0050-6

zbMATH Keywords

nonstandard analysisJordan curve theoremReverse mathematicsSchönflies theoremSecond-order arithmetic

Mathematics Subject Classification ID

Descriptive set theory (03E15) Foundations of classical theories (including reverse mathematics) (03B30) Nonstandard models of arithmetic (03H15) Second- and higher-order arithmetic and fragments (03F35) Nonstandard analysis (26E35)

Related Items (7)

Complex analysis in subsystems of second order arithmetic ⋮ Nonstandard second-order arithmetic and Riemann's mapping theorem ⋮ Tanaka's theorem revisited ⋮ The Brouwer invariance theorems in reverse mathematics ⋮ ERNA and Friedman's Reverse Mathematics ⋮ Formalizing non-standard arguments in second-order arithmetic ⋮ Non-standard analysis in ACA0 and Riemann mapping theorem

Cites Work

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• Uniformly defined descending sequences of degrees
• Non‐standard Analysis in WKL₀
• A non-standard construction of Haar measure and weak König's lemma
• A nonstandard proof of the Jordan curve theorem
• A nonstandard proof of the Jordan curve theorem

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