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Separation and Weak König's Lemma

Published online by Cambridge University Press:  12 March 2014

A. James Humphreys and
Stephen G. Simpson
A. James Humphreys
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, State College, PA 16802, E-mail:, jimbo@math.psu.edu
Stephen G. Simpson
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, State College, PA 16802, E-mail:, simpson@math.psu.edu
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Abstract

We continue the work of [14, 3, 1, 19, 16, 4, 12, 11, 20] 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 WKL0 over RCA0. We show that the separation theorem for separably closed convex sets is equivalent to ACA0 over RCA0. Our strategy for proving these geometrical Hahn–Banach theorems is to reduce to the finite-dimensional case by means of a compactness argument.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 1 , March 1999, pp. 268 - 278
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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