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.
"Degrees of rigidity for Souslin trees." J. Symbolic Logic 74 (2) 423 - 454, June 2009. https://doi.org/10.2178/jsl/1243948321