Talk:Wadge hierarchy

organization

So there are several related topics that could plausibly be article titles:

plus the existing one, Wadge degree.

I think they make perhaps two or three articles, with one "central" or "primary" one that introduces the subject and links to the "secondary" one(s) for more details. What I don't believe is that Wadge degree is the natural choice for the "central" article; I'd think that would be Wadge hierarchy, to show the big picture.

Just a thought for anyone (including me) who might be adding to this article—keep the big picture in mind, even if some of it is currently missing (that is, redlinks). Don't try to force everything under the title Wadge degree just because that's the article that currently exists. --Trovatore 16:33, 1 April 2006 (UTC)[reply]

went ahead and moved it

On second thought, I have my doubts that there's the necessary editor commitment to make more than one article anytime soon (certainly, there's not from me). All topics should probably be at least touched on at Wadge hierarchy, and we can make redirects-with-possibilities for them, to be expanded into articles if anyone gets ambitious. If Wadge degree itself were to be turned into an article, it should probably be about something like the fine analysis of Wadge degrees done by Louveau. --Trovatore 16:49, 1 April 2006 (UTC)[reply]

hierarchy(ies)

I've reverted the change from "a hierarchy" to "multiple hierarchies" (by an anon, unfortunately, so it's hard to find the editor to discuss it). Up to as far as determinacy holds, the Wadge order is linear, with the exception that non-self-dual Wadge degrees are incomparable with their duals. Also the standard term is "Wadge hierarchy", not "Wadge hierarchies".

To tell the truth I'm not even sure what "multiple hierarchies" is supposed to mean. Perhaps the editor who made the change would like to explain on this talk page. --Trovatore 01:39, 14 April 2006 (UTC)[reply]

Isn't there one hierarchy for each Polish space? Ben Standeven 17:13, 1 April 2007 (UTC)[reply]

True, but the Wadge hierarchy is viewed as a single abstract object that can be interpreted for each Polish space. Similarly, we often make reference to the family of Borel sets, even though there is a separate family for each space.Daniel Walker 15:28, 19 July 2007 (UTC)[reply]

Actually now that I think about it, there is possibly an issue here, at least if you look at it in a zoom lens. The Lipschitz degrees, at least, are different between Cantor space and Baire space -- in one of them there is exactly one self-dual degree between any two adjacent pairs of non-self-dual degrees, whereas in the other there are ω such self-dual degrees. Or something like that. I don't know whether there's such a distinction for the Wadge degrees.

And if you apply the continuous-function version of the definition of Wadge degrees to a connected Polish space, like the reals, things come out very different, at least at the low levels. When I was at North Texas this was a question some of us kicked around for a little while, but we didn't come up with anything terribly interesting.

Still, I think "Wadge hierarchy" is the standard term. --Trovatore 19:18, 19 July 2007 (UTC)[reply]

Proposed merger: fold Wadge game into this article

Wadge game is just a stub that is better as section in this article. I propose a merge with a redirect. Alternatively, fill out the stub and make it a real article. davidwr ^09f9(talk) 15:25, 19 May 2007 (UTC)[reply]

I agree.Daniel Walker 15:29, 19 July 2007 (UTC)[reply]

cleanup

I made some improvements (I think) to the page. My knowledge of the Wadge hierarchy is a bit limited and possibly incorrect, so someone with more experience should take a look.Daniel Walker 15:33, 19 July 2007 (UTC)[reply]

cleanup again

There were some mistakes in the page about the Wadge hierarchy that I corrected. About the discussion above, I think that the pages 'Wadge reducibility' and 'Wadge lemma' should be very short and just give the definitions, while there is more to say about the Wadge hierarchy. Also about Wadge determinacy there is quite some work and some open probems that I might add. Philipp, 07-27-07

"Wadge theory"?

Perhaps this article should be moved to Wadge theory? -- Karada 10:59, 27 July 2007 (UTC)[reply]