### 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) |
---|---|

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 |

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### All Science Journal Classification (ASJC) codes

- Logic

### Cite this

*Annals of Pure and Applied Logic*,

*102*(1-3), 139-157. https://doi.org/10.1016/S0168-0072(99)00039-1

}

*Annals of Pure and Applied Logic*, vol. 102, no. 1-3, pp. 139-157. https://doi.org/10.1016/S0168-0072(99)00039-1

**Changing the heights of automorphism towers.** / Hamkins, Joel David; Thomas, Simon.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Changing the heights of automorphism towers

AU - Hamkins, Joel David

AU - Thomas, Simon

PY - 2000/3/3

Y1 - 2000/3/3

N2 - 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 VP.

AB - 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 VP.

UR - http://www.scopus.com/inward/record.url?scp=0346300204&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346300204&partnerID=8YFLogxK

U2 - 10.1016/S0168-0072(99)00039-1

DO - 10.1016/S0168-0072(99)00039-1

M3 - Article

VL - 102

SP - 139

EP - 157

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

SN - 0168-0072

IS - 1-3

ER -