Separation and Weak Konig's Lemma
Humphreys, A. James ; Simpson, Stephen G.
J. Symbolic Logic, Tome 64 (1999) no. 1, p. 268-278 / Harvested from Project Euclid
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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.
Publié le : 1999-03-14
Classification:  
@article{1183745704,
     author = {Humphreys, A. James and Simpson, Stephen G.},
     title = {Separation and Weak Konig's Lemma},
     journal = {J. Symbolic Logic},
     volume = {64},
     number = {1},
     year = {1999},
     pages = { 268-278},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745704}
}

Humphreys, A. James; Simpson, Stephen G. Separation and Weak Konig's Lemma. J. Symbolic Logic, Tome 64 (1999) no. 1, pp.  268-278. http://gdmltest.u-ga.fr/item/1183745704/