- G. Fuchs and J. D. Hamkins, “Degrees of rigidity for Souslin trees,” J.~Symbolic Logic, vol. 74, iss. 2, pp. 423-454, 2009.
`@ARTICLE{FuchsHamkins2009:DegreesOfRigidity, AUTHOR = {Fuchs, Gunter and Hamkins, Joel David}, TITLE = {Degrees of rigidity for {S}ouslin trees}, JOURNAL = {J.~Symbolic Logic}, FJOURNAL = {Journal of Symbolic Logic}, VOLUME = {74}, YEAR = {2009}, NUMBER = {2}, PAGES = {423--454}, ISSN = {0022-4812}, CODEN = {JSYLA6}, MRCLASS = {03E05}, MRNUMBER = {2518565 (2010i:03049)}, MRREVIEWER = {Stefan Geschke}, URL = {http://wp.me/p5M0LV-3A}, doi = {10.2178/jsl/1243948321}, eprint = {math/0602482}, archivePrefix = {arXiv}, primaryClass = {math.LO}, file = F, }`

We investigate various strong notions of rigidity for Souslin trees, separating them under Diamond into a hierarchy. Applying our methods to the automorphism tower problem in group theory, we show under Diamond that there is a group whose automorphism tower is highly malleable by forcing.