Degrees of rigidity for Souslin trees

Journal of Symbolic Logic 74 (2):423-454 (2009)
Abstract
We investigate various strong notions of rigidity for Souslin trees, separating them under ♢ into a hierarchy. Applying our methods to the automorphism tower problem in group theory, we show under ♢ that there is a group whose automorphism tower is highly malleable by forcing
Keywords Rigid Souslin trees   diamond   automorphism tower
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