Complex analysis in subsystems of second order arithmetic

Abstract. This research is motivated by the program of Reverse Mathematics. We investigate basic part of complex analysis within some weak subsystems of second order arithmetic, in order to determine what kind of set existence axioms are needed to prove theorems of basic analysis. We are especially concerned with Cauchy’s integral theorem. We show that a weak version of Cauchy’s integral theorem is proved in RCA0. Using this, we can prove that holomorphic functions are analytic in RCA0. On the other hand, we show that a full version of Cauchy’s integral theorem cannot be proved in RCA0 but is equivalent to weak K¨onig’s lemma over RCA0.

• Type: Journal
• Year: 2007
• Where: AML
• Authors: Keita Yokoyama
• Keywords: AML 2007, Cauchy’s Integral Theorem, Reverse Mathematics, Weak Subsystems