CONTINUOUS FIRST ORDER LOGIC AND LOCAL STABILITY
By I. Yaacov, Alexander Usvyatsov. 2008
212 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e044af735b18707d678d41a6b8c8882bc3713a2b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- H. Jerome Keisler
- David Sherman
- Ilijas Farah
- Bradd Hart
- Ehud Hrushovski
- I. Yaacov
- Pierre Simon
- Hans Adler
In Computational Theory and Mathematics
- Ehud Hrushovski
- H. Jerome Keisler
- David Sherman
- Ilijas Farah
- Bradd Hart
- I. Yaacov
- Pierre Simon
- Anand Pillay
In Geometry and Topology
- Bradd Hart
- Ehud Hrushovski
- David Sherman
- H. Jerome Keisler
- Ilijas Farah
- I. Yaacov
- Anand Pillay
- Pierre Simon
Citations in the corpus
- Saturation and isomorphism of abstract harmonic spaces (2026, unknown): “Parallel to these analytic achievements, continuous model theory has emerged as a comprehensive language for metric structures, developed by Chang and Keisler [CK66], Ben Yaacov, Usvyatsov, Pedersen [BYU07, BYU10, BYP10], and others.”
- RANDOMIZATIONS OF MODELS AS METRIC STRUCTURES (2009, methodology): “This fact was given a direct proof in [ BU ].”
- Stable group theory and approximate subgroups (2009, background): “3; compare also [47], §3, and the stability section in [1].”
- Model theory of operator algebras II: model theory (2010, methodology): “It is entirely equivalent to the multi-sorted version of continuous logic as introduced in [3] but has some characteristics which are more suited for applications.”