Talk:Borel hierarchy

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Mathematics rating:	B Class	Mid Priority	Field: Foundations, logic, and set theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Could be more accessible with stronger lead. Not sure this is B yet. Geometry guy 22:43, 15 June 2007 (UTC)

[edit] Plans

The plan is to expand this into a description of at least the boldface Borel hierarchy on a Polish space, including Sigma^0_a etc. But there is some doubt about how to deal with the lightface Borel sets -- do they go here, or in arithmetical hierarchy or somewhere else? CMummert 13:59, 13 June 2006 (UTC)

[edit] rank

Is the definition

The rank of a Borel set is the least α such that the set is in .

really canonical? Do we have a reference? I could not find it in Kechris' book, nor in Moschovakis'. The definition

the least α such that the set is in

seems equally plausible. I have seen the expression "Borel set of finite rank" used, but at the moment cannot recall a place where (if ever) I have seen "Borel set of rank alpha".

--Aleph4 15:19, 1 April 2007 (UTC)

You may be right. I replaced the def with a def of "finite rank" which is less problematic and probably more relevant to the reader. CMummert · talk 19:20, 1 April 2007 (UTC)