Complex analysis in subsystems of second order arithmetic
type: Item
instance of: scholarly article
title: Complex analysis in subsystems of second order arithmetic
zbMATH Open document ID: 1112.03053
author: Keita Yokoyama
published in: Archive for Mathematical Logic
publication date: 2007-02-14T00:00:00Z
review text: This article, based on the author's masters thesis, formulates several theorems of complex analysis and analyzes them in the framework of reverse mathematics. The code for a holomorphic function includes its derivative, and the code for an analytic function includes its power series expansion. Using this encoding, RCA\(_0\) suffices to prove that the class of holomorphic functions and the class analytic functions are identical. The author proves in RCA\(_0\) a version of Cauchy's integral theorem restricted to functions with moduli of uniform continuity, and shows that a more general formulation of Cauchy's integral theorem is equivalent to WKL\(_0\). The article also includes a proof in RCA\(_0\) of Morera's theorem, a number of other results, and a reference to a preprint on a reverse mathematical analysis of the Jordan curve theorem.
reviewed by: Jeffry L. Hirst
Mathematics Subject Classification ID: 03F35
Mathematics Subject Classification ID: 03B30
zbMATH DE Number: 5126638
zbMATH Keywords: second-order arithmetic
zbMATH Keywords: reverse mathematics
zbMATH Keywords: Cauchy's integral theorem
zbMATH Keywords: holomorphic functions
zbMATH Keywords: analytic functions
zbMATH Keywords: Morera's theorem
MaRDI profile type: Publication
full work available at URL: s00153-006-0017-z
OpenAlex ID: W2039034939
cites work: Q5535091
cites work: The mean value theorem in second order arithmetic
cites work: The strong soundness theorem for real closed fields and Hilbert's Nullstellensatz in second order arithmetic
cites work: The Jordan curve theorem and the Schönflies theorem in weak second-order arithmetic
cites work: Fixed point theory in weak second-order arithmetic
cites work: Q4220572
cites work: Measure theory and weak König's lemma
DOI: 10.1007/S00153-006-0017-Z
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description: scientific article; zbMATH DE number 5126638