# Sh:1020

- Shelah, S., & Usvyatsov, A. (2019).
*Minimal stable types in Banach spaces*. Adv. Math.,**355**, 106738, 29. arXiv: 1402.6513 DOI: 10.1016/j.aim.2019.106738 MR: 3994442 -
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 \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. - published version (29p)

Bib entry

@article{Sh:1020, author = {Shelah, Saharon and Usvyatsov, Alexander}, title = {{Minimal stable types in Banach spaces}}, journal = {Adv. Math.}, fjournal = {Advances in Mathematics}, volume = {355}, year = {2019}, pages = {106738, 29}, issn = {0001-8708}, mrnumber = {3994442}, mrclass = {03C45 (46B20)}, doi = {10.1016/j.aim.2019.106738}, note = {\href{https://arxiv.org/abs/1402.6513}{arXiv: 1402.6513}}, arxiv_number = {1402.6513} }