### Banach spaces and groups - order properties and universal models

by Shelah and Usvyatsov. [ShUs:789]

Israel J Math, 2006

We deal with two natural examples of almost-elementary classes:
the class of all Banach spaces (over R or 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.

Back to the list of publications