Changing the heights of automorphism towers

Annals of Pure and Applied Logic 102 (1-2):139-157 (2000)

Joel David Hamkins
Oxford University
If G is a centreless group, then τ denotes the height of the automorphism tower of G. We prove that it is consistent that for every cardinal λ and every ordinal α<λ, there exists a centreless group G such that τ=α; and if β is any ordinal such that 1β<λ, then there exists a notion of forcing , which preserves cofinalities and cardinalities, such that τ=β in the corresponding generic extension
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DOI 10.1016/s0168-0072(99)00039-1
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