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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: 774 Registered: 7/12/10
Re: Possible major blunder in Rado's version of Canonical Ramsey
Theorem that goes far beyond omitting proof steps

Posted: Nov 10, 2013 4:53 AM

On Friday, November 8, 2013 10:53:07 AM UTC, David Hartley wrote:
>
> <pepstein5@gmail.com> writes
>

> >You are absolutely correct about the purpose of the theorem. David and
>
> >I are of the opinion that the non-vacuity of the definition is
>
> >sufficiently obvious to the intended readership, as not to be worth
>
> >stating.
>
>
>
> Well, I wouldn't object to him stating it, but to spending several lines
>
> on the proof while skipping much less obvious steps in the proof of the
>
> main theorem. Just "the map f defined by ... is an obvious, indeed
>
> 'canonical', example of an L-canonical map on any B contained in A".
>

But there's a _fundamental_ problem with the whole paper that goes far beyond omitting some details, and overemphasizing others.

One of his two main purposes is apparently to give a simpler proof of the original Erdos--Rado version of Canonical Ramsey. The original paper is available here: http://www.renyi.hu/~p_erdos/1950-01.pdf

Agreed that, (when amended using the contributions on this thread), the newer approach is simpler. But it also proves _far less_. The original Erdos-Rado version doesn't assume the axiom of choice (referred to as "Zermelo's axiom" in that paper). However, the newer paper does assume the axiom of countable choice by asserting the existence of B' = {b0, b1...}

I'm sure that Erdos could have given a particularly simple presentation if he didn't care about avoiding choice.

The fact that one version is choice-free and the other isn't needed to be mentioned in the Rado paper referred to at the beginning of the thread.

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
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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