Continuous first order logic and local stability

Itaï Ben Yaacov, Alexander Usvyatsov

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)5213-5259
Number of pages47
JournalTransactions of the American Mathematical Society
Issue number10
StatePublished - Oct 2010
Externally publishedYes


  • Continuous logic
  • Local stability
  • Metric structures
  • Stability


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