We investigate the strength of set existence axioms needed for separable Banach space theory. We show that a very strong axiom, Π 1 1 comprehension , is needed to prove such basic facts as the existence of the weak-* closure of any norm-closed subspace of 1 = c * 0. This is in contrast to earlier work [6, 4, 7, 23, 22] in which theorems of separable Banach… (More)
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… (More)
When was the last time you did something for the first time?-Fight Club Choose your road. Ride it well. List of Papers This thesis is based on the following papers, which are referred to in the text by their Roman numerals. Reprints were made with permission from the publishers.