Source: Notre Dame J. Formal Logic Volume 53, Number 2
(2012), 155-174.
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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References
Fuchs, G., "Closed maximality principles: Implications, separations and combinations", The Journal of Symbolic Logic, vol. 73 (2008), pp. 276–308.
Fuchs, G., and J. D. Hamkins, "Changing the heights of automorphism towers by forcing with Souslin trees over $L$", The Journal of Symbolic Logic, vol. 73 (2008), pp. 614–33.
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Mathematical Reviews (MathSciNet):
MR801316
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