ON UNIFORM CANONICAL BASES IN Lp LATTICES AND OTHER METRIC

Description

ON UNIFORM CANONICAL BASES IN Lp LATTICES AND OTHER METRIC STRUCTURES ITAÏ BEN YAACOV Abstract. We discuss the notion of uniform canonical bases, both in an abstract manner and specif- ically 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. Introduction In stability theory, the canonical base of a type is a minimal set of parameters required to define the type, and as such it generalises notions such as the field of definition of a variety in algebraic geometry. Just like the field of definition, the canonical base is usually considered as a set, a point of view which renders it a relatively coarse invariant of the type. We may ask, for example, whether a type is definable over a given set (i.e., whether the set contains the canonical base), or whether the canonical base, as a set, is equal to some other set. However, canonical bases, viewed as sets, cannot by any means classify types over a given model of the theory, and they may very well by equal for two distinct types.

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Sujets

• Uniform
• Definable
• Indeed.com

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 18

Extrait

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