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Topic: Surprise at my failure to resolve an issue in an elementary paper by Rado
Replies: 44   Last Post: Nov 10, 2013 12:23 PM

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 David Hartley Posts: 463 Registered: 12/13/04
Re: Possible major blunder in Rado's version of Canonical Ramsey Theorem that goes far beyond omitting proof steps
Posted: Nov 10, 2013 9:50 AM

<pepstein5@gmail.com> writes
>No, B' is a subset of A which is not countable, in general.

Third line of Rado's paper: "Let A = (0,1,2,...}"

As far as I know (which isn't far) Ramsey's theorem only applies to
countable sets so Rado's proof will only work with countable A.

>repetition of my point. In summary, the Erdos-Rado result proves
>Canonical Ramsey without AC whereas Rado deduces Canonical Ramsey from
>AC.

I don't agree. Both papers prove the Canonical Theorem from the standard
Ramsey theorem without any further use of AC. As long as Ramsey's
theorem can be proved without AC, so can the Canonical theorem.

--
David Hartley

Date Subject Author
11/3/13 Paul
11/3/13 David Hartley
11/3/13 fom
11/3/13 fom
11/3/13 fom
11/4/13 fom
11/4/13 Paul
11/4/13 Paul
11/4/13 Peter Percival
11/4/13 David Hartley
11/4/13 Paul
11/4/13 David Hartley
11/4/13 Paul
11/4/13 David Hartley
11/4/13 Paul
11/5/13 Paul
11/5/13 David Hartley
11/5/13 Paul
11/5/13 David Hartley
11/5/13 Paul
11/6/13 Paul
11/6/13 Paul
11/7/13 Paul
11/7/13 David Hartley
11/7/13 Paul
11/7/13 David Hartley
11/7/13 Paul
11/7/13 David Hartley
11/7/13 David Hartley
11/7/13 Paul
11/7/13 David Hartley
11/8/13 Paul
11/8/13 David Hartley
11/7/13 Paul
11/7/13 fom
11/8/13 Paul
11/8/13 David Hartley
11/10/13 Paul
11/10/13 David Hartley
11/10/13 Paul
11/10/13 David Hartley
11/10/13 David Hartley
11/10/13 Paul
11/4/13 Paul
11/4/13 Peter Percival