Re: A question

[Josef Urban <urban@ktilinux.ms.mff.cuni.cz>]

It seems I forgot about limit cardinalities, what I wrote holds up to
first uncountable limit cardinal. So the hypothesis is probably 
false, depending on what you mean by the last "etc." :-).

JU

On Sat, 2 Jun 2001, Josef Urban wrote:

> 
> 
> 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
>