Journal of Symbolic Logic 64 (1):268-278 (1999)

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 WKL 0 over RCA 0 . We show that the separation theorem for separably closed convex 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
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DOI 10.2307/2586763
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References found in this work BETA

Fragments of Arithmetic.Wilfried Sieg - 1985 - Annals of Pure and Applied Logic 28 (1):33-71.
Located Sets and Reverse Mathematics.Mariagnese Giusto & Stephen G. Simpson - 2000 - Journal of Symbolic Logic 65 (3):1451-1480.
Fixed Point Theory in Weak Second-Order Arithmetic.Naoki Shioji & Kazuyuki Tanaka - 1990 - Annals of Pure and Applied Logic 47 (2):167-188.

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Citations of this work BETA

How Incomputable Is the Separable Hahn-Banach Theorem?Guido Gherardi & Alberto Marcone - 2009 - Notre Dame Journal of Formal Logic 50 (4):393-425.
Fundamental Notions of Analysis in Subsystems of Second-Order Arithmetic.Jeremy Avigad - 2006 - Annals of Pure and Applied Logic 139 (1):138-184.

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