Minimal types in stable Banach spaces
Logic
2019-08-20 v2
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.
Cite
@article{arxiv.1402.6513,
title = {Minimal types in stable Banach spaces},
author = {Saharon Shelah and Alexander Usvyatsov},
journal= {arXiv preprint arXiv:1402.6513},
year = {2019}
}