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Re: Uncountable List
Posted:
Dec 31, 2012 1:55 AM


On Dec 30, 9:22 pm, William Elliot <ma...@panix.com> wrote: > On Sun, 30 Dec 2012, David C. Ullrich wrote: > > William Elliot <ma...@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?
If you're still talking about lists of infinite binary sequences, then the answer (assuming the axiom of choice) is the initial ordinal omega_{alpha + 1} where alpha is the ordinal such that c = aleph_{alpha}. But that's the answer given in the post you were replying to, so I guess you're looking for some other kind of answer.



