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Topic: Given a set , is there a disjoint set with an arbitrary cardinality?
Replies: 28   Last Post: Dec 4, 2012 5:50 PM

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 Carsten Schultz Posts: 3 Registered: 11/29/12
Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted: Dec 3, 2012 10:07 AM

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

Date Subject Author
12/3/12 jaakov
12/3/12 forbisgaryg@gmail.com
12/3/12 Aatu Koskensilta
12/3/12 jaakov
12/3/12 Carsten Schultz
12/3/12 jaakov
12/3/12 Aatu Koskensilta
12/3/12 jaakov
12/3/12 Aatu Koskensilta
12/3/12 jaakov
12/3/12 Carsten Schultz
12/3/12 jaakov
12/3/12 Aatu Koskensilta
12/3/12 Butch Malahide
12/3/12 jaakov
12/3/12 Butch Malahide
12/4/12 jaakov
12/4/12 forbisgaryg@gmail.com
12/4/12 William Elliot
12/4/12 forbisgaryg@gmail.com
12/4/12 William Elliot
12/4/12 William Elliot
12/4/12 jaakov
12/4/12 William Elliot
12/4/12 jaakov
12/4/12 Shmuel (Seymour J.) Metz
12/4/12 Spammer
12/4/12 jaakov