Model theory and its applications: dependent classes

Objectif

Model theory deals with general classes of structures (called models).
Specific examples of such classes are: the class of rings or the class of
algebraically closed fields.

It turns out that counting the so-called complete types over models in the
class has an important role in the development of model theory in general and
stability theory in particular.
Stable classes are those with relatively few complete types (over structures
from the class); understanding stable classes has been central in model theory
and its applications.

Recently, I have proved a new dichotomy among the unstable classes:
Instead of counting all the complete types, they are counted up to conjugacy.
Classes which have few types up to conjugacy are proved to be so-called
``dependent'' classes (which have also been called NIP classes).
I have developed (under reasonable restrictions) a ``recounting theorem'',
parallel to the basic theorems of stability theory.

I have started to develop some of the basic properties of this new approach.
The goal of the current project is to develop systematically the theory of
dependent classes. The above mentioned results give strong indication that this
new theory can be eventually as useful as the (by now the classical) stability
theory. In particular, it covers many well known classes which stability theory
cannot treat.

Régime de financement

ERC-AG - ERC Advanced Grant

Institution d’accueil

THE HEBREW UNIVERSITY OF JERUSALEM

Contribution de l’UE

€ 1 748 000,00

Adresse

EDMOND J SAFRA CAMPUS GIVAT RAM
91904 Jerusalem
Israël

Type d’activité

Higher or Secondary Education Establishments

Contact administratif

Hani Ben-Yehuda (Ms.)

Chercheur principal

Saharon Shelah (Prof.)

Liens

Contacter l’organisation Site web

Coût total

Aucune donnée

Bénéficiaires (1)

THE HEBREW UNIVERSITY OF JERUSALEM

Israël