Date: Dec 30, 2012 10:22 PM
Author: William Elliot
Subject: Re: Uncountable List

On Sun, 30 Dec 2012, David C. Ullrich wrote:
> William Elliot <marsh@panix.com> wrote:
>

> >How long does an uncountable list with no duplicates,
> >of infinite binary sequences (IBS) have to be to force
> >the list to contain all the IBS's?

>
> It's obvious that there is no length long enough to force this. A "list"
> of length c (the cardinality of the set of infinite binary sequences)
> need not contain all the sequences, and a list of length greater than c
> must contain duplicates (and still need not contain all the sequences).


Whoops.

How long does an uncountable list have
to be before it must contain a duplicate?