## Notre Dame Journal of Formal Logic

### Iteratively Changing the Heights of Automorphism Towers

#### 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

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

Digital Object Identifier
doi:10.1215/00294527-1715662

Mathematical Reviews number (MathSciNet)
MR2925274

Zentralblatt MATH identifier
1258.03069

#### 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

#### References

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