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

Mathematics – Logic

Scientific paper

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23 pages

Scientific paper

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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