On uniform canonical bases in Lp lattices and other metric structures
Abstract
We discuss the notion of uniform canonical bases, both in an abstract manner and specifically for the theory of atomless Lp 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.
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