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anyone mind if i update the "A Game for the Borel Functions" link in the references section? the link doesn't work in dare.uva.nl it's my own work so i'm not sure whether this is a breach of etiquette (changing signature) Drderevo ( talk) 06:48, 11 November 2013 (UTC)
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)
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)
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)
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)
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)
I agree. Daniel Walker 15:29, 19 July 2007 (UTC)
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)
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. Miaoku, 07-27-07
Would it make sense to move this article to Wadge theory? -- Karada 10:59, 27 July 2007 (UTC)
I'm thinking that at this stage it would be appropriate to remove the "in need of expert" and "clean-up" tags at the beginning of the page. What does everyone think?
Also, I'm putting in a "cite sources" tag. If someone with a better math library than mine could find specific sources for the claims made it would go a long way to "spiffying" this page up. Daniel Walker 17:43, 9 August 2007 (UTC)
I just reorganized most of what I wrote earlier and added a little more. I apologize for any mistakes. I'm also removing the tags since I think (1) there are enough references, and (2) I tried to format everything. Since I'm new at wiki I'm not sure if this is good style so feel free to add tags again or make changes. I also thought from "references" you should be able to find most of the statements, and further reading is the rest, that's why I regrouped it. Does somebody want to write a page about "Rabin degree" etc? I don't know what it is... If not, would it be better to delete the links?
What about "Wadge degree" for a title? It seems that the word "hierarchy" suggests it's well founded (which is only the case in Baire space (and Cantor space etc.) and if you assume enough determinacy), while "degree" sounds more general to me... -- Miaoku 02:22, 11 August 2007 (UTC)
In "See also" I have deleted "Veblen hierarchy" - although (a variant of) the Veblen function appears in computing the length of initial segments of the Wadge hierarchy, the Veblen hierarchy itself doesn't seem to be connected with the Wadge hierarchy. I also deleted "Rabin index", because there don't seem to be a lot of connections between Wadge degrees and this (although I don't know anything about the Rabin index, I just looked up its definition in a paper), please feel free to revert this if you think different. "Steel hierarchy" I also removed, since this seems to be a very specialized topic and I'm not sure if anything will be written(?) Miaoku 10:52, 12 August 2007 (UTC)
Removed the category: game theory, since in my view, there is (nearly) no connection between the games used in set theory and game theory in the usual sense. Miaoku 09:21, 22 August 2007 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
anyone mind if i update the "A Game for the Borel Functions" link in the references section? the link doesn't work in dare.uva.nl it's my own work so i'm not sure whether this is a breach of etiquette (changing signature) Drderevo ( talk) 06:48, 11 November 2013 (UTC)
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)
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)
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)
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)
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)
I agree. Daniel Walker 15:29, 19 July 2007 (UTC)
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)
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. Miaoku, 07-27-07
Would it make sense to move this article to Wadge theory? -- Karada 10:59, 27 July 2007 (UTC)
I'm thinking that at this stage it would be appropriate to remove the "in need of expert" and "clean-up" tags at the beginning of the page. What does everyone think?
Also, I'm putting in a "cite sources" tag. If someone with a better math library than mine could find specific sources for the claims made it would go a long way to "spiffying" this page up. Daniel Walker 17:43, 9 August 2007 (UTC)
I just reorganized most of what I wrote earlier and added a little more. I apologize for any mistakes. I'm also removing the tags since I think (1) there are enough references, and (2) I tried to format everything. Since I'm new at wiki I'm not sure if this is good style so feel free to add tags again or make changes. I also thought from "references" you should be able to find most of the statements, and further reading is the rest, that's why I regrouped it. Does somebody want to write a page about "Rabin degree" etc? I don't know what it is... If not, would it be better to delete the links?
What about "Wadge degree" for a title? It seems that the word "hierarchy" suggests it's well founded (which is only the case in Baire space (and Cantor space etc.) and if you assume enough determinacy), while "degree" sounds more general to me... -- Miaoku 02:22, 11 August 2007 (UTC)
In "See also" I have deleted "Veblen hierarchy" - although (a variant of) the Veblen function appears in computing the length of initial segments of the Wadge hierarchy, the Veblen hierarchy itself doesn't seem to be connected with the Wadge hierarchy. I also deleted "Rabin index", because there don't seem to be a lot of connections between Wadge degrees and this (although I don't know anything about the Rabin index, I just looked up its definition in a paper), please feel free to revert this if you think different. "Steel hierarchy" I also removed, since this seems to be a very specialized topic and I'm not sure if anything will be written(?) Miaoku 10:52, 12 August 2007 (UTC)
Removed the category: game theory, since in my view, there is (nearly) no connection between the games used in set theory and game theory in the usual sense. Miaoku 09:21, 22 August 2007 (UTC)