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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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Paul

Posts: 434
Registered: 7/12/10
Re: The Rado paper -- a possible further simplification
Posted: Nov 8, 2013 4:08 AM
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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')
>
> --
>


I think I can offer a tiny further improvement in your simplification as follows. In contrast to Rado, the set on which we show canonicity is B(4) rather than B(2). Your lemma 1 can then be used unchanged because B(4) is a subset of B(2).
This approach lets us omit the step:
[Replace X and X' by X_0 and X_1 from [B(4)]^r such that (X,X') = (X_0,X_1)]

Does this work as a further simplification or does it simplify too much, and thereby introduce an error?

Many thanks for your help and comments.

Paul Epstein


Date Subject Author
11/3/13
Read Surprise at my failure to resolve an issue in an elementary paper by Rado
Paul
11/3/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/3/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
fom
11/3/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
fom
11/3/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
fom
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
fom
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Peter Percival
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/5/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/5/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/5/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/5/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/5/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/6/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/6/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
Paul
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
David Hartley
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
Paul
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
David Hartley
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
Paul
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
David Hartley
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
David Hartley
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
Paul
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
David Hartley
11/8/13
Read Re: The Rado paper -- a possible further simplification
Paul
11/8/13
Read Re: The Rado paper -- a possible further simplification
David Hartley
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
Paul
11/7/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
fom
11/8/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/8/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/10/13
Read Re: Possible major blunder in Rado's version of Canonical Ramsey
Theorem that goes far beyond omitting proof steps
Paul
11/10/13
Read Re: Possible major blunder in Rado's version of Canonical Ramsey Theorem that goes far beyond omitting proof steps
David Hartley
11/10/13
Read Re: Possible major blunder in Rado's version of Canonical Ramsey
Theorem that goes far beyond omitting proof steps
Paul
11/10/13
Read Re: Possible major blunder in Rado's version of Canonical Ramsey Theorem that goes far beyond omitting proof steps
David Hartley
11/10/13
Read Re: Possible major blunder in Rado's version of Canonical Ramsey Theorem that goes far beyond omitting proof steps
David Hartley
11/10/13
Read Re: Possible major blunder in Rado's version of Canonical Ramsey
Theorem that goes far beyond omitting proof steps
Paul
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Peter Percival

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