Well-Ordering Hereditarily Finite Sets

  • Thread starter Dragonfall
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Main Question or Discussion Point

Does there exist a recursive well-ordering of the hereditarily finite sets?
 

Answers and Replies

CRGreathouse
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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 ({}, {{}}, {{{}}}, {{}, {{}}}, ...)
 
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Excellent. Thanks.
 

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