Notre Dame Journal of Formal Logic

Iteratively Changing the Heights of Automorphism Towers

Gunter Fuchs and Philipp Lücke

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.

Article information

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

Dates
First available in Project Euclid: 9 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1336588247

Digital Object Identifier
doi:10.1215/00294527-1715662

Mathematical Reviews number (MathSciNet)
MR2925274

Zentralblatt MATH identifier
1258.03069

Subjects
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]

Keywords
automorphism tower forcing maximality principle

Citation

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. https://projecteuclid.org/euclid.ndjfl/1336588247


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References

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