Non‐standard analysis in ACA0 and Riemann mapping theorem

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. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)