Banach spaces and groups - Order properties and universal models

Saharon Shelah*, Alex Usvyatsov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

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 that both of these classes do not have the strict order property, and find the exact place of each one of them in Shelah's SOPn (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 density characters.

Original languageEnglish
Pages (from-to)245-270
Number of pages26
JournalIsrael Journal of Mathematics
Volume152
DOIs
StatePublished - 2006

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