Separation and Weak König's Lemma
A. James Humphreys
Stephen G. Simpson
Pennsylvania State University
October 25, 1998
Simpson's research was partially supported by NSF grant DMS-9303478.
This paper has been accepted October 10, 1997 for publication in
the Journal of Symbolic Logic.
We continue the work of
investigating 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
that the separation theorem for separably closed convex sets is
Our strategy for proving these
geometrical Hahn-Banach theorems is to reduce to the
finite-dimensional case by means of a compactness argument.
Stephen G Simpson