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April 24th, 2010, 04:39 PM   #1
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cardinality, ZFC

Prove that has cardinality . Which axioms of ZFC are satisfied by ?

Here, for a given cardinal , denotes the collection of sets whose transitive closure has cardinality less than . Also, is defined by , , , if .

I do not have any good ideas on how to prove this. I would appreciate a few hints. Thanks.

Link:
http://en.wikipedia.org/wiki/Zermelo%E2 ... The_axioms

Problem statement:
http://i719.photobucket.com/albums/ww19 ... 1272155858
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