2015/12/29 by Karim Khanaki, Khanaki, Karim · 1 citation
Mathematics · #Advanced Topology and Set Theory #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1512.08691
In \citeK3 we pointed out the correspondence between a result of Shelah in model theory, i.e. a theory is unstable if and only if it has IP or SOP, and the well known compactness theorem of Eberlein and Šmulian in functional analysis. In this paper, we relate a \em natural Banach space V to a formula ϕ(x,y), and show that ϕ is stable (resp NIP, NSOP) if and only if V is reflexive (resp Rosenthal, weakly sequentially complete) Banach space. Also, we present a proof of the Eberlein-Šmulian theorem by a model theoretic approach using Ramsey theorems which is illustrative to show some correspondences between model theory and Banach space theory.