On d-finiteness in continuous structures

• Autorzy: Itaï Ben Yaacov , Alexander Usvyatsov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03C95: Abstract model theory
• 03C35: Categoricity and completeness of theories
• 03C45: Classification theory, stability and related concepts
• 03C90: Nonclassical models (Boolean-valued, sheaf, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 194
• Numer: 1
• Strony: 67-88

Daty

wydano

2007

Twórcy

autor

Itaï Ben Yaacov

• Université de Lyon, Université Lyon 1, Institut Camille Jordan, CNRS, UMR 5208, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France

autor

Alexander Usvyatsov

• Mathematics Department, UCLA, Box 951555OC, Los Angeles, CA 90095-1555, U.S.A.

Identyfikatory

DOI

10.4064/fm194-1-4