Re: A question

["Antoni Urban" <antoniu@softm.co.za>]

Thanks Josef (with the same name Urban, family?) for your answer. It was
after I sent my question, when I decided to study the subject of Cardinal
Numbers. I have gone through Mizar Library and found interesting papers by
Grzegorz Bancerek and yourself.

Thanks once again - Antoni Urban



----- Original Message -----
From: Josef Urban <urban@ktilinux.ms.mff.cuni.cz>
To: <mizar-forum@mizar.uwb.edu.pl>
Sent: Saturday, June 02, 2001 12:58 PM
Subject: Re: A question


>
>
> 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
> >
>
>