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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