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Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted:
Dec 3, 2012 10:07 AM
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Am 03.12.12 15:21, schrieb jaakov:
> 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?
>
I am not sure if I understand all of this.
Consider the class of all ordinals not in X. This is a well-ordered
proper class and hence has an initial segment which is order isomorphic
to k. Take that initial segment.
hth
Carsten
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