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

Published online by Cambridge University Press:  12 March 2014

Gunter Fuchs  and
Joel David Hamkins
Gunter Fuchs
Affiliation:
Westfälische Wilhelms-Universität Mùnster, Institut Für Mathematische Logik Und Grundlagenforschung, Einsteinstraβe 62, 48149 Munster., Germany, E-mail: gfuchs@math.uni-muenster.de
Joel David Hamkins
Affiliation:
Mathematics Program, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY 10016., USA, E-mail: jdh@hamkins.org
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 2 , June 2008 , pp. 614 - 633
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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