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Topic: Anti-foundation axiom
Replies: 11   Last Post: Mar 15, 2013 6:00 AM

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Shmuel (Seymour J.) Metz

Posts: 3,331
Registered: 12/4/04
Re: Anti-foundation axiom
Posted: Mar 12, 2013 10:40 PM
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In <JLidnXKtPoy3A6LMnZ2dnUVZ5h-dnZ2d@giganews.com>, on 03/12/2013
at 02:28 PM, "K_h" <KHolmes@SX729.com> said:

>This is not a correct characterization of set theory. In the
>generally accepted approach, not everything is a set and no
>collection can be a member of itself. Collections are bifurcated
>into two types and they are sets and proper classes. So
>"Everything is a set" just isn't part of modern theory.


There is no "everything" in modern set theory. What you have described
applies to GBN but not to ZFC, where the universe of discourse
includes only sets.

>Controversy exists over whether or not there exists
>non-constructible sets,


Controversy exists over whether to allow axiom systems that permit
non-constructible sets, but there is no controversy over whether there
are non-constructible sets in, e.g., ZFC.

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

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