GALOIS GROUPS OF FIRST ORDER THEORIES

We study the groups GalL(T) and GalKP(T), and the associated equivalence relations EL and EKP, attached to a first order theory T. An example is given where EL≠ EKP (a non G-compact theory). It is proved that EKP is the composition of EL and the closure of EL. Other examples are given showing this is best possible.