Paul
Posts:
763
Registered:
7/12/10


Re: Another notcompletelyinsignificant 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: > In message <86eb8927154a4ad2906f759e79de59d9@googlegroups.com>, Paul > > <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 Lcanonical. 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 Lcanonical, only Lcanonical on B, > > presumably he means here Lcanonical 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

