On uniform canonical bases in $L_p$ lattices and other metric structures

Itaï Ben Yaacov (1)

1 ICJ - Institut Camille Jordan

We discuss the notion of \emph{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.

Mots clés: stable theory; uniform canonical base; $L_p$ Banach lattice; beautiful pairs

Domaines: Logique [math.LO]

Itaï Ben Yaacov. On uniform canonical bases in $L_p$ lattices and other metric structures. Journal of Logic and Analysis, 2012, 4 (12), pp.1-30. ⟨10.4115/jla.2012.4.12⟩. ⟨hal-00512369v2⟩