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

Gunter Fuchs·Joel David Hamkins
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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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Gunter Fuchs, Joel David Hamkins. 2007-02-26. Changing the Heights of Automorphism Towers by Forcing with Souslin Trees over L. https://arxiv.org/abs/math/0702768

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