Degrees of rigidity for Souslin trees

  • 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://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.

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