Banach spaces and groups - order properties and universal models

2003/03/26 by Saharon Shelah, Shelah, Saharon, Alexander Usvyatsov +2
Computer Science · Mathematics · #Digital Image Processing Techniques #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.math/0303325

published as Israel J. Math. 152 (2006) 245--270

arxiv created 2003/03/26 · openalex publication_date 2003/03/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

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