Degrees of rigidity for Souslin trees

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Journal of Symbolic Logic 74 (2):423-454 (2009)
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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

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10.2178/jsl/1243948321

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Joel David Hamkins
Oxford University

Citations of this work

Algebraicity and Implicit Definability in Set Theory.Joel David Hamkins & Cole Leahy - 2016 - Notre Dame Journal of Formal Logic 57 (3):431-439.
Club degrees of rigidity and almost Kurepa trees.Gunter Fuchs - 2013 - Archive for Mathematical Logic 52 (1-2):47-66.
On the rigidity of Souslin trees and their generic branches.Hossein Lamei Ramandi - 2022 - Archive for Mathematical Logic 62 (3):419-426.
Souslin algebra embeddings.Gido Scharfenberger-Fabian - 2011 - Archive for Mathematical Logic 50 (1-2):75-113.

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Changing the heights of automorphism towers.Joel David Hamkins & Simon Thomas - 2000 - Annals of Pure and Applied Logic 102 (1-2):139-157.

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