Submission date: 29 December 2015.

Abstract:

In [K3] 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 Smulian in functional analysis. In this paper, we relate a 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-Smulian theorem by a model theoretic approach using Ramsey theorems which is illustrative to show some correspondences between model theory and Banach space theory.

Mathematics Subject Classification: 03C45, 46E15, 46B50

Keywords and phrases:

Full text arXiv 1512.08691: pdf, ps.