Talk:Projective hierarchy

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 Field: Foundations, logic, and set theory


This used to be a redirect to analytical hierarchy, but that doesn't make any sense as "analytical" is a lightface notion, whereas "projective" is boldface. This page and analytic set are candidates for a future merge into the pointclass page, when I get that written. --Trovatore 8 July 2005 06:19 (UTC)

Requested move[edit]

Projective setProjective hierarchy

There's no sense in having both articles, and the "hierarchy" title better reflects the content. --Trovatore 06:56, 31 March 2007 (UTC)

Done. CMummert · talk 14:02, 31 March 2007 (UTC)
I think it is nice to have a separation between X hierarchy and X set. For example:
Arithmetical hierarchy / Arithmetical set
Analytical hierarchy / Analytic set
Borel hierarchy / Borel set (= Borel algebra)
There is a little duplication of content, but I think it is helpful to a naive reader to start with the non-hierarchy definition and later learn about the stratification. CMummert · talk 14:06, 31 March 2007 (UTC)
Well, you can make a case for that, but it does make maintenance and improvement more difficult. (By the way the "analytical hierarchy/analytic set" juxtaposition is wrong.) --Trovatore 16:37, 31 March 2007 (UTC)
The Lightface and darkface page is still unwritten. Not being a descriptive set theorist, I tend mentally identify the corresponding hierarchies.CMummert · talk 17:18, 31 March 2007 (UTC)
There's a pointclass page that treats that material, with redirects from lightface, lightface pointclass, boldface pointclass, and a link from boldface (disambiguation). No one seems to have touched that page but me. I think it's a critical concept, given that it's the essential subject matter of descriptive set theory (one could almost say it should bear the same relation to the descriptive set theory article that set bears to set theory). I think I did a decent start-class job on the article, but I wonder whether people are actually using the material, given that no one has edited it. --Trovatore 07:11, 1 April 2007 (UTC)
And thanks for reverting me at Analytic set, I remembed the distinction when I added it to analytical hierarchy but not this morning. I wasn't thinking. CMummert · talk 18:27, 31 March 2007 (UTC)