Well-Ordering Hereditarily Finite Sets

[Dragonfall]

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

 

[CRGreathouse]

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 ({}, {{}}, {{{}}}, {{}, {{}}}, ...)

 

[Dragonfall]

Excellent. Thanks.