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Degrees of rigidity for Souslin trees

Published online by Cambridge University Press:  12 March 2014

Gunter Fuchs  and
Joel David Hamkins
Gunter Fuchs
Affiliation:
Westfälische Wilhelms-Universität Münster, Institut für Mathematische Logik und Grundlagenforschung, Einsteinstraße 62, 48149 Münster, Germany, E-mail: [email protected] Mathematics, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, Ny 10016, USA
Joel David Hamkins
Affiliation:
Mathematics, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, Ny 10016, USA Mathematics, The College of Staten Island of Cuny, Staten Island, Ny 10314, USA, E-mail: [email protected], URL: http://jdh.hamkins.org
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Abstract

We investigate various strong notions of rigidity for Souslin trees, separating them under ⟡ into a hierarchy. Applying our methods to the automorphism tower problem in group theory, we show under ⟡ that there is a group whose automorphism tower is highly malleable by forcing.

Keywords

Rigid Souslin treesdiamondautomorphism tower
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 2 , June 2009 , pp. 423 - 454
Copyright
Copyright © Association for Symbolic Logic 2009

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