Wikipedia: History of Ultrafilter Lemma

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Changed: 5c5

The problem with this proof is that it uses Zorn's Lemma, which is equivalent to the axiom of choice. While it cannot be proven from ZF (the Zermelo-Frankel axioms) alone, it cannot be used to prove the axiom of choice, so it is properly weaker.

This proof uses Zorn's Lemma, which is equivalent to the axiom of choice. The Ultrafilter Lemma cannot be proven from ZF (the Zermelo-Frankel axioms) alone, and it cannot be used to prove the axiom of choice, so it is properly weaker.

	Revision 5 . . December 17, 2001 4:06 am by AxelBoldt
	Revision 4 . . (edit) October 1, 2001 1:09 am by Zundark [minor tidying of formulae]