### Iteratively Changing the Heights of Automorphism Towers

Gunter Fuchs and Philipp Lücke
Source: Notre Dame J. Formal Logic Volume 53, Number 2 (2012), 155-174.

#### Abstract

We extend the results of Hamkins and Thomas concerning the malleability of automorphism tower heights of groups by forcing. We show that any reasonable sequence of ordinals can be realized as the automorphism tower heights of a certain group in consecutive forcing extensions or ground models, as desired. For example, it is possible to increase the height of the automorphism tower by passing to a forcing extension, then increase it further by passing to a ground model, and then decrease it by passing to a further forcing extension, and so on, transfinitely. We make sense of the limit models occurring in such a sequence of models. At limit stages, the automorphism tower height will always be 1.

First Page:
Primary Subjects: 03E75, 03E40, 03E57, 20E36, 20F28
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1336588247
Digital Object Identifier: doi:10.1215/00294527-1715662
Mathematical Reviews number (MathSciNet): MR2925274
Zentralblatt MATH identifier: 06054422

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