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2012 Iteratively Changing the Heights of Automorphism Towers
Gunter Fuchs, Philipp Lücke
Notre Dame J. Formal Logic 53(2): 155-174 (2012). DOI: 10.1215/00294527-1715662


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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Gunter Fuchs. Philipp Lücke. "Iteratively Changing the Heights of Automorphism Towers." Notre Dame J. Formal Logic 53 (2) 155 - 174, 2012.


Published: 2012
First available in Project Euclid: 9 May 2012

zbMATH: 1258.03069
MathSciNet: MR2925274
Digital Object Identifier: 10.1215/00294527-1715662

Primary: 03E40 , 03E57 , 03E75 , 20E36 , 20F28

Keywords: automorphism tower , Forcing , maximality principle

Rights: Copyright © 2012 University of Notre Dame


Vol.53 • No. 2 • 2012
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