Axiom of Regularity:

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From: zuhair on 12 Jan 2010 21:16

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Hi all,

Is the following axiom equivalent to the axiom of Regularity?

Axiom: For all x ( For all y (y e TC(x) -> ~ y e TC(y)) &
For all y (y e TC(x) -> 0 e TC(y)) ).

were "TC" stands for "Transitive closure" defined in the
standard manner, and "0" stands for the empty set.

More specifically is (ZF minus Regularity) + the above axiom
equivalent to ZF ?

Zuhair

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