Hereditarily Symmetric Sets and the Set of Odd Numbers

Discussion in 'Math Research' started by Dr Tim, Sep 25, 2009.

  1. Dr Tim

    Dr Tim Guest

    Hereditarily Symmetric Sets is a non-standard model of set theory in
    which the Axiom of Choice is false.
    The idea is that all permitted sets have asymmetries of only finite
    depth.

    But I am having difficulty grasping the details.
    Can anyone tell me if the set of odd numbers is an HS set,
    and if so, how this symmetry manifests itself under the transposition
    of 0 and 1?

    {1, 3, 5, ...} -> {0, 3, 5,...}, so the symmetry must be at a lower
    layer.
    And that's where I get stuck.

    Thanks!
     
    Dr Tim, Sep 25, 2009
    #1
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