Date: Dec 3, 2012 9:21 AM Author: jaakov Subject: Given a set , is there a disjoint set with an arbitrary cardinality? Dear all:

Given a set X and a cardinal k, is there a set Y such that card(Y)=k and

X is disjoint from Y?

Is there a proof of this fact that works without the axiom of regularity

(= axiom of foundation) and does not assume purity of sets?

Thanks in advance

Jaakov.

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