Forcing a Boolean algebra with predesigned automorphism group

Abstract

For suitable groups G G we will show that one can add a Boolean algebra B B by forcing in such a way that A u t ( B ) Aut(B) is almost isomorphic to G G . In particular, we will give a positive answer to the following question due to J. Roitman: Is ℵ ω \aleph _{\omega } a possible number of automorphisms of a rich Boolean algebra?