On d-finiteness in continuous structures

Itaï Ben Yaacov, Alexander Usvyatsov

Research output: Contribution to journalArticlepeer-review


We observe that certain classical results of first order model theory fail in the context of continuous first order logic. We argue that this happens since finite tuples in a continuous structure may behave as infinite tuples in classical model theory. The notion of a d-finite tuple attempts to capture some aspects of the classical finite tuple behaviour. We show that many classical results involving finite tuples are valid in continuous logic upon replacing "finite" with "d-finite". Other results, such as Vaught's no two models theorem and Lachlan's theorem on the number of countable models of a superstable theory are proved under the assumption of enough (uniformly) d-finite tuples.

Original languageEnglish
Pages (from-to)67-88
Number of pages22
JournalFundamenta Mathematicae
Issue number1
StatePublished - 2007
Externally publishedYes


  • Approximately w-saturated model
  • Continuous first order logic
  • Model theory of metric structures
  • d-finite tuple


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