Changing the heights of automorphism towers by forcing with Souslin trees over $L$

[bibtex key=FuchsHamkins2008:ChangingHeightsOverL]

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.

In an earlier paper with Simon Thomas, “Changing the heights of automorphism towers,”¬†we had added such malleable groups by forcing, and the current paper addresses the question as to whether there are such groups already in L.

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