Minimal stable types in Banach spaces

Saharon Shelah, Alexander Usvyatsov

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number106738
JournalAdvances in Mathematics
StatePublished - 15 Oct 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.


  • Banach spaces
  • Categoricity
  • Continuous model theory
  • Hilbert spaces
  • Stability
  • Wide types


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