Minimal types in the stable Banach spaces

by Shelah and Usvyatsov. [ShUs:1020]
Advances in Math, 2008-09-25
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 ell_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.

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