Obiettivo Model theory deals with general classes of structures (called models).Specific examples of such classes are: the class of rings or the class ofalgebraically closed fields.It turns out that counting the so-called complete types over models in theclass has an important role in the development of model theory in general andstability theory in particular.Stable classes are those with relatively few complete types (over structuresfrom the class); understanding stable classes has been central in model theoryand 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 ofdependent classes. The above mentioned results give strong indication that thisnew theory can be eventually as useful as the (by now the classical) stabilitytheory. In particular, it covers many well known classes which stability theorycannot treat. Campo scientifico natural sciencesmathematicspure mathematicsdiscrete mathematicsmathematical logic Programma(i) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Argomento(i) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Invito a presentare proposte ERC-2013-ADG Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-AG - ERC Advanced Grant Istituzione ospitante THE HEBREW UNIVERSITY OF JERUSALEM Contributo UE € 1 748 000,00 Indirizzo EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem Israele Mostra sulla mappa Tipo di attività Higher or Secondary Education Establishments Contatto amministrativo Hani Ben-Yehuda (Ms.) Ricercatore principale Saharon Shelah (Prof.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato Beneficiari (1) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto THE HEBREW UNIVERSITY OF JERUSALEM Israele Contributo UE € 1 748 000,00 Indirizzo EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem Mostra sulla mappa Tipo di attività Higher or Secondary Education Establishments Contatto amministrativo Hani Ben-Yehuda (Ms.) Ricercatore principale Saharon Shelah (Prof.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato