Apparaît dans la collection : 2018 - T1 - WS3 - Model theory and applications

A theory T is said to have exact saturation at a (usually singular) cardinal κ if there is a model which is κ- saturated but not κ +- saturated. T has PC-exact saturation at κ if for every T1 containing T (of the same cardinality), there is a model of T1 whose reduct to the language of T is κ-saturated but not κ +-saturated. In a previous work (with Shelah and Simon) we identified exact saturation in simple in NIP theories. By work of Shelah and Malliaris, if a theory has SOP2 then it does not have PC exact saturation. In this talk I will discuss PC exact saturation in the context of simple theories, and also the local analog.