STABLE BANACH SPACES AND BANACH SPACE STRUCTURES, II: FORKING AND COMPACT TOPOLOGIES

Abstract

. We study model theoretical stability for structures from functional analysis. We prove a functional-analytic version of the Finite Equivalence Relation Theorem. We also the Stability Spectrum Theorem for Banach space structures. 1. INTRODUCTION In [3], we introduced the notion of model theoretical stability for Banach space structures and gave several characterizations of stability. Here we study further properties of stable theories. In Sections 3 and 4 we introduce the concept forking for positive bounded formulas and prove some properties which characterize forking. The proofs in these sections are direct adaptations of the corresponding proofs in classical model theory, but we include them for completeness. In Section 5 we prove a functional analytic version of the Finite Equivalence Relation Theorem: Theorem. Let p # S n (A) and q 1 and q 2 be two distinct nonforking extensions of p over a model E containing A. Then, if N > #p#, there exists a pseudometric # on (B N ) n ...