Minimal stable types in Banach spaces

Saharon Shelah; Alexander Usvyatsov

doi:10.1016/j.aim.2019.106738

Minimal stable types in Banach spaces

Saharon Shelah, Alexander Usvyatsov

Research output: Contribution to journal › Article › peer-review

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 ℓ₂ 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.

Original language	English
Article number	106738
Journal	Advances in Mathematics
Volume	355
DOIs	https://doi.org/10.1016/j.aim.2019.106738
State	Published - 15 Oct 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

Banach spaces
Categoricity
Continuous model theory
Hilbert spaces
Stability
Wide types

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10.1016/j.aim.2019.106738

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Minimal stable types in Banach spaces

Abstract

Bibliographical note

Keywords

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