Date: August 14, 1997
Title: Separation and Weak K"onig's Lemma
Authors: A. James Humphreys, Stephen G. Simpson
Author e-mail: simpson@math.psu.edu
Available: http://www.math.psu.edu/simpson/papers/sep.ps
Format: PostScript file (AMS-LaTeX source is also available)
Publication: accepted October 10, 1997 for publication in the Jounal
of Symbolic Logic
Abstract: This paper is a contribution to the program of Reverse
Mathematics. Continuing earlier work of Brown and others, we
investigate the strength of set existence axioms needed for separable
Banach space theory. We show that the separation theorem for open
convex sets is equivalent to WKL_0 over RCA_0. We show that the
separation theorem for separably closed sets is equivalent to ACA_0
over RCA_0. Our strategy for proving these geometrical Hahn-Banach
theorems is to reduce to the finite-dimensional case by means of a
compactness argument.