PILLAY'S ALTERNATIVE DEFINITION FOR WEAK ELIMINATION OF IMAGINARIES COINCIDES WITH POIZAT'S ORIGINAL ONE (Model theoretic aspects of the notion of independence and dimension)

The smallest algebraically closed set which appears in Poizat's original definition for WEI coincides with algebraic closure of finite real tuple which appears in Pillay's alternative definition for WEI

PAC structures as invariants of finite group actions

We study model theory of actions of finite groups on substructures of a stable structure. We give an abstract description of existentially closed actions as above in terms of invariants and PAC structures. We show that if the corresponding PAC property is first order, then the theory of such actions has a model companion. Then, we analyze some particular theories of interest (mostly various theories of fields of positive characteristic) and show that in all the cases considered the PAC property is first order