### Abstract

If G is a centreless group, then τ(G) 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 (a) τ(G)=α; and (b) if β is any ordinal such that 1≤β<λ, then there exists a notion of forcing P, which preserves cofinalities and cardinalities, such that τ(G)=β in the corresponding generic extension V^{P}.

Original language | English (US) |
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Pages (from-to) | 139-157 |

Number of pages | 19 |

Journal | Annals of Pure and Applied Logic |

Volume | 102 |

Issue number | 1-3 |

DOIs | |

State | Published - Mar 3 2000 |

### All Science Journal Classification (ASJC) codes

- Logic

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## Cite this

Hamkins, J. D., & Thomas, S. (2000). Changing the heights of automorphism towers.

*Annals of Pure and Applied Logic*,*102*(1-3), 139-157. https://doi.org/10.1016/S0168-0072(99)00039-1