Changing the heights of automorphism towers by forcing with Souslin trees over L
Changing the heights of automorphism towers by forcing with Souslin trees over L
Abstract We prove that there are groups in the constructible universe whose automorphism towers are highly malleable by forcing. This is a consequence of the fact that, under a suitable diamond hypothesis, there are sufficiently many highly rigid non-isomorphic Souslin trees whose isomorphism relation can be precisely controlled by forcing.