Non-standard analysis in ACA0 and Riemann mapping theorem

Abstract. This research is motivated by the program of Reverse Mathematics and non-standard arguments in second-order arithmetic. Within a weak subsystem of second order arithmetic ACA0, we investigate some aspects of non-standard analysis related to sequential compactness. Then, using arguments of non-standard analysis, we show the equivalence of the Riemann mapping theorem and ACA0 over WKL0.

• Type: Journal
• Year: 2007
• Where: MLQ
• Authors: Keita Yokoyama
• Keywords: MLQ 2007, Non-standard Analysis, Non-standard Arguments, Second-order Arithmetic