• G. Fuchs and J. D. Hamkins, “Degrees of rigidity for Souslin trees,” J.~Symbolic Logic, vol. 74, iss. 2, pp. 423-454, 2009.  
  Journal MR Citation arχiv

  @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://dx.doi.org/10.2178/jsl/1243948321},
  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.