Date: Mar 31, 2013 12:49 PM
Author: ross.finlayson@gmail.com
Subject: Re: Matheology § 224

On Mar 31, 9:17 am, fom <fomJ...@nyms.net> wrote:
> On 3/31/2013 10:52 AM, Ross A. Finlayson wrote:
>
>
>

> > Well, you see Virgil has introduced a term in context the "binary
> > rational path":  in cooperative communication that is so defined
> > there, because that every initial segment is the initial segment of a
> > rational, and that the language of "rational paths" is unbounded,
> > doesn't offer for him the conclusion of his arguments.  So, he expects
> > that to be understood as his definition in passing, or he can point to
> > it later, as to differentiating his personal definition from the
> > general definition, as so qualified.

>
> Yeah.
>
> He should not have done that.
>
> The Baire space has the required property in
> relation to rational numbers -- correspondence
> with eventually constant sequences.
>
> It gets confusing when you are trying to deal
> with WM's misrepresentations.


Where "the" Baire space for Rene-Louis Baire is N^N as opposed to the
general property of a space being Baire, consider whether there are
ordinals between n, for any n in N, and N. N^n <-> N, N^N <-> P(N).
if there are no ordinals between n and N, are there no cardinals
betwen those of N^n and N^N? Because, cardinals have initial
ordinals. Are there limit ordinals between those of w^n and w^N?
Obviously enough it's consistent with ZF that there are, though, there
are none between n, for all n e N, and N.

Then, compared to the language of the expansions of 2^w from the
alphabet {0,1} as (0|1)\infty, items from N^N are in a language (n e
N)\infty.

What's the 1-1 and onto function from 2^w to N^N?

Then, apply EF or sweep to it.

Thanks,

Ross Finlayson