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Topic: Using classes instead of sets
Replies: 26   Last Post: Apr 1, 2013 8:04 PM

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Shmuel (Seymour J.) Metz

Posts: 3,271
Registered: 12/4/04
Re: Using classes instead of sets
Posted: Mar 30, 2013 10:13 PM
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In <o_qdnc1PnJYA9MvMnZ2dnUVZ_rOdnZ2d@giganews.com>, on 03/29/2013
at 11:26 PM, fom <fomJUNK@nyms.net> said:

>Can you name one?

New foundations has a universal set. However, {x|P(x}} only exists in
NF if P is stratified. I don't know whether there is a Category Theory
equivalent.

>I suppose in that regard, there may be (some standard set theory)+
>(some large cardinal axiom) combination that constitutes a set
>theory different from ZFC for which your statement holds.


No; if you start with ZF then you can't have a universal set, even if
you have large cardinals.

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