Changing the Heights of Automorphism Towers by Forcing with Souslin Trees over L
Günter Fuchs, Joel David Hamkins · arXiv (Cornell University) · 2007
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.