Sh:789

• Shelah, S., & Usvyatsov, A. (2006). Banach spaces and groups—order properties and universal models. Israel J. Math., 152, 245–270. arXiv: math/0303325 DOI: 10.1007/BF02771986 MR: 2214463
• Abstract:
  We deal with two natural examples of almost-elementary classes: the class of all Banach spaces (over {\mathbb R} or {\mathbb C}) and the class of all groups. We show both of these classes do not have the strict order property, and find the exact place of each one of them in Shelah’s SOP_n (strong order property of order n) hierarchy. Remembering the connection between this hierarchy and the existence of universal models, we conclude, for example, that there are “few” universal Banach spaces (under isometry) of regular cardinalities.
• Version 2005-01-20_11 (19p) published version (26p)

@article{Sh:789,
 author = {Shelah, Saharon and Usvyatsov, Alexander},
 title = {{Banach spaces and groups---order properties and universal models}},
 journal = {Israel J. Math.},
 fjournal = {Israel Journal of Mathematics},
 volume = {152},
 year = {2006},
 pages = {245--270},
 issn = {0021-2172},
 mrnumber = {2214463},
 mrclass = {03C45 (20A05 46B99)},
 doi = {10.1007/BF02771986},
 note = {\href{https://arxiv.org/abs/math/0303325}{arXiv: math/0303325}},
 arxiv_number = {math/0303325}
}