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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: 780 Registered: 7/12/10
Re: Another not-completely-insignificant gap in the Rado paper
Posted: Nov 7, 2013 6:12 AM

On Wednesday, November 6, 2013 12:10:46 AM UTC, David Hartley wrote:
>
> <pepstein5@gmail.com> writes
>

> >Of course, the below is irrelevant to understanding the proof. However,
>
> >I am completely mystified by the page 1 sentences: "We now show that f
>
> >is L-canonical. We shall apply the definition of f repeatedly without
>
> >referring to this fact." It's only the second of those sentences that
>
> >confuses me. The first sentence is given for context.
>
>
>
> I can't make sense of it either. The whole section is rather odd.
>
> Firstly he hasn't actually defined L-canonical, only L-canonical on B,
>
> presumably he means here L-canonical on A. The actual theorem is trivial
>
> yet he devotes several lines to a proof. I assume Bulletin articles are
>
> supposed to be short, so it would have been much better to use that
>
> space for a more detailed proof of the important theorem. In particular
>
> explaining the step that had us both confused.
>
>
>
> The idea is lovely, the presentation is not.
>

So far, even when I appeal to large xi terms, I don't see enough space between the elements to be sure of obtaining the relationships of the form [X0, X1] = [X1, X2] etc.

However, I think I see the issue. As written, I don't see where he uses the fact that B is a proper subset of B'.

Therefore, perhaps the definition of B(t) is an error? Perhaps the element at index j in the sequence B(t) is intended to mean the term at index j in the C sequence where C refers to the sequence: b0, b2, b4, b6....

There does seem to be some small problem either with the paper, or my understanding of the paper, because I see no place in the paper where he uses the fact that he has removed the odd index elements from B'.

Perhaps he redefined the b_i elements so that the i index now refers to their position in B rather than in B' but he definitely needs to tell the reader that he is doing this.

I see that you need to remove the odd elements because I don't get enough spacing, but the construction still doesn't seem coherent because the [X0, X1] steps simply don't work if you follow the definitions literally.

Thank you for your help and insights.

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