Re: Request for Peer Review - Refutation of Cantor Theorem Conclusion

Arturo Magidin wrote:
In article <1146239905.551887.306000@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Scott <ToaTerra@xxxxxxxxx> wrote:
....
Can you explain how the diagonal avoids being in the power set? Do you
regard it as not being a set, or do you think it contains some element
that is not in the base set?

If D is an element of the powerset, then the powerset/set-theory is
inconsistency. (Its a proof by contradiction.)


That's a tall order. Since the fact that D is an element of the power
set is a trivial consequence of the axioms of ZF, you are saying much
more than just that you have disproven the conclusion of Cantor's
Theorem: you are asserting that you have proven that Zermelo-Fraenkel
Set Theory is inconsistent!


Looking over some of his messages, I think Scott may be starting out by
assuming there is a surjection from N onto P(N). Cantor's Theorem does
prove an inconsistency in a set theory that adds that, as an additional
axiom, to ZF.

Patricia
.

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