Martin Hils (Paris): Generic automorphisms and expansions of algebraically closed fields
Freitag, 03.07.2009 16:15 im Raum SR 8
In this talk, we will address the question for which theories T the class of models of T with a generic automorphism is elementary (in this case the corresponding theory is denoted by TA and we say that "TA exists"). Usually, for theories of Fraisse limits, like dense linear orders or the theory of the random graph, TA does not exist.
We will first give some general facts about generic automorphisms, discuss examples of theories where TA does not exist and then mention a criterion which is sufficient for TA to exist in case T is a stable theory. Finally, we apply this criterion to various
expansions of algebraically closed fields, in particular to Poizat's "green fields" and bad fields. As a corollary, we show that there exists what might be called a "bad pseudofinite field" in characteristic 0.