TY - JOUR
T1 - Changing the heights of automorphism towers
AU - Hamkins, Joel David
AU - Thomas, Simon
N1 - Funding Information: E-mail address: sthomas@mathrutgers.edu (S. Thomas) 1The research was partially supported by a grant from Research Foundation. 2The research was partially supported by NSF Grants.
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.
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U2 - https://doi.org/10.1016/S0168-0072(99)00039-1
DO - https://doi.org/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 -