Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Paul Posts: 780 Registered: 7/12/10
Re: Another not-completely-insignificant gap in the Rado paper
Posted: Nov 7, 2013 6:02 PM

On Thursday, November 7, 2013 9:50:35 PM UTC, David Hartley wrote:
> In message <7vKtBqDeeAfSFwPl@212648.invalid>, David Hartley
>
> <me9@privacy.net> writes
>

> >Replace X and X' by X_0 and X_1 from [B(4)]^r such that (X,X') =
>
> >(X_0,X_1) and f(X) = f(X_0), f(X') = f(X_1)(as in Rado's proof). Let
>
> >X_0^sigma = b_4p. Form X_2 from X_0 by replacing X_0^sigma by b_(4p+2).
>
> >Since sigma is not in L, f(X_0) = f(X_2). X_1^rho = X_0^sigma is not in
>
> >X_2 so the lemma can be applied to X_2 and X_1, giving f(X_2) =/=
>
> >f(x_1) and so f(X_0) =/= f(X_1).
>
> >
>
> >Hope there's no mistakes.
>
>
>
> Well I've spotted one mistake already. We can only select X_0 and X_1 to
>
> get (X,X') = (X_0,X_1) not to also have f(X) = f(X_0), f(X') = f(X_1).
>
> But it doesn't matter, that's enough for f(X_0) =/= f(X_1) to imply f(X)
>
> =/= f(X')
>

David,

Thanks. I did check this carefully and it seems fine. Much better than in the paper.

Finally, I won't need to be sceptical if someone accosts me in the street and tells me. "Verily I say unto you: The Canonical Ramsey theorem is absolutely true."

Paul Epstein

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