  We show that for an arbitrary stable theory T, a group G is profinite if and
only if G occurs as a Galois group of some Galois extension inside a monster
model of T.
  We prove that any PAC substructure of the monster model of T has projective
absolute Galois group. Moreover, any projective profinite group G is isomorphic
to the absolute Galois group of some substructure P of the monster model. If T
is omega-stable, then P can be chosen to be PAC.
  Finally, we provide a description of some Galois groups of existentially
closed substructures with G-action in the terms of the universal Frattini
cover. Such structures might be understood as a new examples of PAC structures.
