Re: A question

[Josef Urban <urban@mail.kolej.mff.cuni.cz>]

Being no expert and assuming that the N^N in your notation  has the usual
meaning (functions from N to N), I think your hypothesis (assuming AC ...
Axiom of Choice ... so that each set had some cardinality) reduces to GCH
... General Continuum Hypothesis, which sais following:
For each infinite cardinal M the cardinality of successor of M is equal to
the cardinality of 2^M.
This hypothesis as well as its contradiction are relatively consistent
with the usual axioms of set theory.

I suggest reading some chapters on cardinal arithmetics and hierarchy in
some set theory textbook to get more on this and clarify the notation.

Best Regards,
Josef Urban


On Fri, 1 Jun 2001, Antoni Urban wrote:

> Hi
>
> Piotr's problem has been sorted out. What I am asking for is somehow
> relating. See the attachment.
>
> Regards - Antoni Urban