Pablo Cubides-Kovacsics:
Stably embedded pairs and applications
Zeit und Ort
Mittwoch, 11.9.19, 16:00-17:00, Raum 318, Ernst-Zermelo-Str. 1
Zusammenfassung
A structure is called stably embedded if the trace of every externally definable is definable\nwith parameters from the structure. We will show different examples of theories for which the class of pairs of\nelementary substructures, where the smaller one is stably embedded in the bigger one, forms an elementary class\nin the language of pairs. When, in addition, the model-theoretic algebraic closure of a set is a model of the\ntheory, we show that definable types are uniformly definable. As an application, we obtain uniform definability\nof types in various NIP theories including the theory of algebraically closed valued fields, real closed valued\nfields, p-adically closed fields and Presburger arithmetic. This implies in return that the spaces of definable\ntypes in such theories are pro-definable.