Weak forms of elimination of imaginaries

We study the degree of elimination of imaginaries needed for the three main applications: to have canonical bases for types over models, to define strong types as types over algebraically closed sets and to have a Galois correspondence between definably closed sets B such that A subset of or equal to B subset of or equal to acl(A) and closed subgroups of the Galois group Aut(acl(A)/A). We also characterize when the topology of the Galois group is the quotient topology. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim.