Notre Dame Journal of Formal Logic

Iteratively Changing the Heights of Automorphism Towers

Gunter Fuchs and Philipp Lücke


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.

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Notre Dame J. Formal Logic, Volume 53, Number 2 (2012), 155-174.

First available in Project Euclid: 9 May 2012

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Zentralblatt MATH identifier

Primary: 03E75: Applications of set theory 03E40: Other aspects of forcing and Boolean-valued models 03E57: Generic absoluteness and forcing axioms [See also 03E50] 20E36: Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45] 20F28: Automorphism groups of groups [See also 20E36]

automorphism tower forcing maximality principle


Fuchs, Gunter; Lücke, Philipp. Iteratively Changing the Heights of Automorphism Towers. Notre Dame J. Formal Logic 53 (2012), no. 2, 155--174. doi:10.1215/00294527-1715662.

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