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Well-Ordering Hereditarily Finite Sets

  1. Apr 22, 2008 #1
    Does there exist a recursive well-ordering of the hereditarily finite sets?
  2. jcsd
  3. Apr 22, 2008 #2


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    Sure. At each step in the construction, only a finite number of sets are added; these can be ordered as desired (lexiographically, say).

    The natural well-order is then ({}, {{}}, {{{}}}, {{}, {{}}}, ...)
  4. Apr 22, 2008 #3
    Excellent. Thanks.
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