Francesco Gallinaro:
Dividing lines in positive model theory
Time and place
Tuesday, 25.10.22, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
Abstract
Positive logic is first-order logic where formulas are built without negation and using only existential quantifiers. By choosing the right languages to work with, this turns out to be a proper generalization of first-order logic. It is then natural to ask how much of usual model theory we can transfer to this setting; for example, one might ask about the dividing lines in classification theory, such as stability and simplicity: these notions, mostly introduced by Shelah, have been fruitfully used to classify theories with respect to various properties, for example the number of their models in a given cardinality or the existence of certain independence relations.\nIn this talk I will briefly introduce positive model theory and some of the ideas about dividing lines, before discussing some work in progress (joint with Anna Dmitrieva and Mark Kamsma) about their interplay.