Author:
Humphreys A. James,Simpson Stephen G.
Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
Reference20 articles.
1. Fixed point theory in weak second-order arithmetic
2. Humphreys A. James , On the Necessary Use of Strong Set Existence Axioms in Analysis and Functional Analysis, Ph.D. thesis , The Pennsylvania State University, 1996, viii + 83 pages.
3. Which set existence axioms are needed to prove the separable Hahn-Banach theorem?
Cited by
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