Well-Ordering Hereditarily Finite Sets

1. Apr 22, 2008

Dragonfall

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

2. Apr 22, 2008

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

3. Apr 22, 2008

Dragonfall

Excellent. Thanks.