Date: Mar 30, 2013 10:13 PM
Author: Shmuel (Seymour J.) Metz
Subject: Re: Using classes instead of sets

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.

--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

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