Re: Separation,Power and Countability.

On Jun 15, 6:04 pm, zuhair <zaljo...@xxxxxxxxx> wrote:

Cantor's proof is that: for any injective function f from w to P(w)
there will always exist a subset of w that is not in the range of > f,
and this subset is defined using separation as {x|xew & ~xef(x)}
The formula ~xef(x) is not a formula in ONE free variable!

It can easily be rendered such by Existential Elimination in the
course of the proof of Cantor's theorem; this does not prevent from
proving Cantor's theorem in Z.

So, definability plus your restricted separation would yield
inconsistency.


.

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