
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


In message <12c8ad0bd2994ad4bb3cfe26efe30ae5@googlegroups.com>, Paul <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.
>Your initial point about ErdosRado stating that they avoid AC is a >repetition of my point. In summary, the ErdosRado 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

