Changing the Heights of Automorphism Towers by Forcing with Souslin Trees over L

Journal of Symbolic Logic 73 (2):614 - 633 (2008)
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
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