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Continuous first order logic and local stability. (English) Zbl 1200.03024

Summary: We develop continuous first-order logic, a variant of the logic described by Chang and Keisler (1966). 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.

MSC:

03C90 Nonclassical models (Boolean-valued, sheaf, etc.)
03C45 Classification theory, stability, and related concepts in model theory
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