Minimal types in stable Banach spaces

Abstract

We prove existence of wide types in a continuous theory expanding a Banach space, and density of minimal wide types among stable types in such a theory. We show that every minimal wide stable type is "generically" isometric to an l_2 space. We conclude with a proof of the following formulation of Henson's Conjecture: every model of an uncountably categorical theory expanding a Banach space is prime over a spreading model, isometric to the standard basis of a Hilbert space.

References in corpus (2)

• Continuous first order logic and local stability
• Morley sequences in dependent theories

Cited by in corpus (3)

• Vaught's Two-Cardinal Theorem and Quasi-Minimality in Continuous Logic
• Asymptotically Hilbertian Modular Banach Spaces: Examples of Uncountable Categoricity
• Indiscernible Subspaces and Minimal Wide Types