Continuous first order logic and local stability

Itaï Ben Yaacov (1) , Alexander Usvyatsov (2)

1 ICJ - Institut Camille Jordan
2 Department of Mathematics [UCLA]

We develop continuous first order logic, a variant of the logic described in \cite{Chang-Keisler:ContinuousModelTheory}. We show that this logic has the same power of expression as the framework of open Hausdorff cats, and as such extends Henson's logic for Banach space structures. We conclude with the development of local stability, for which this logic is particularly well-suited.

Mots clés: continuous logic; metric structures; stability; local stability

Domaines: Logique [math.LO]

Itaï Ben Yaacov, Alexander Usvyatsov. Continuous first order logic and local stability. Transactions of the American Mathematical Society, 2010, 362 (10), pp.5213-5259. ⟨10.1090/S0002-9947-10-04837-3⟩. ⟨hal-00220454⟩