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On uniform canonical bases in \(L_p\) lattices and other metric structures. (English) Zbl 1285.03032

Summary: We discuss the notion of uniform canonical bases, both in an abstract manner and specifically for the theory of atomless \(L_p\) lattices. We also discuss the connection between the definability of the set of uniform canonical bases and the existence of the theory of beautiful pairs (i.e., with the finite cover property), and prove in particular that the set of uniform canonical bases is definable in algebraically closed metric valued fields.

MSC:

03C45 Classification theory, stability, and related concepts in model theory
12J05 Normed fields
12J10 Valued fields
46B42 Banach lattices
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