The rigid relation principle, a new weak choice principle

  • J. D. Hamkins and J. Palumbo, “The rigid relation principle, a new weak choice principle,” Mathematical Logic Quarterly, vol. 58, iss. 6, pp. 394-398, 2012.  
    @ARTICLE{HamkinsPalumbo2012:TheRigidRelationPrincipleANewWeakACPrinciple,
    AUTHOR = {Joel David Hamkins and Justin Palumbo},
    TITLE = {The rigid relation principle, a new weak choice principle},
    JOURNAL = {Mathematical Logic Quarterly},
    YEAR = {2012},
    volume = {58},
    number = {6},
    pages = {394--398},
    ISSN = {0942-5616},
    month = {},
    note = {},
    url = {http://jdh.hamkins.org/therigidrelationprincipleanewweakacprinciple/},
    eprint = {1106.4635},
    archivePrefix = {arXiv},
    primaryClass = {math.LO},
    doi = {10.1002/malq.201100081},
    MRNUMBER = {2997028},
    MRREVIEWER = {Eleftherios C.~Tachtsis},
    abstract = {},
    keywords = {},
    source = {},
    }

The rigid relation principle, introduced in this article, asserts that every set admits a rigid binary relation. This follows from the axiom of choice, because well-orders are rigid, but we prove that it is neither equivalent to the axiom of choice nor provable in Zermelo-Fraenkel set theory without the axiom of choice. Thus, it is a new weak choice principle. Nevertheless, the restriction of the principle to sets of reals (among other general instances) is provable without the axiom of choice.

This paper arose out of my related mathoverflow question:  Does every set admit a rigid binary relation (and how is this related to the axiom of choice)?