Well-Ordering Hereditarily Finite Sets

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Thread starter Dragonfall
Start date Apr 22, 2008
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Dragonfall

Thread starter
Apr 22, 2008

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

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CRGreathouse

Science Advisor

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Apr 22, 2008

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

Apr 22, 2008

Excellent. Thanks.

Well-Ordering Hereditarily Finite Sets

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Well-Ordering Hereditarily Finite Sets

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