Complex analysis in subsystems of second order arithmetic
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.
scientific article; zbMATH DE number 5126638
scientific article