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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: Another not-completely-insignificant gap in the Rado paper
Posted: Nov 7, 2013 4:50 PM

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 Hartley

Date Subject Author
11/3/13 Paul
11/3/13 David Hartley
11/3/13 fom
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