Talk:Analytical hierarchy
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Problem here -- the boldface/lightface distinction is not clearly made --Trovatore 7 July 2005 19:31 (UTC)
The term "analytical" refers exclusively to the lightface concept, whereas "projective" is a boldface notion. Therefore "projective set" should not redirect here. I'm planning a pointclass page where it might redirect instead. Also "analytic" and "co-analytic", which are boldface notions, should be removed from this page. --Trovatore 7 July 2005 20:35 (UTC)
The other major problem with this page is the conflation of formulas and sets. Consider for example the following passage:
- A
formula is a formula of the form 
, where X is now a predicate and 
, while a set is a set of the form
,
- where S is Borel and R is a relation.
First, the definition is incorrect, because no restriction is placed on the definability of R. But the problem that more exemplifies the difficulty with the page as a whole is that nothing is said about the underlying Polish space. --Trovatore 7 July 2005 20:48 (UTC)
[edit] major problems seem to be fixed
Accuracy tag removed (thanks to Ben Standeven). Tech tag removed; subject is inherently technical. --Trovatore 02:18, 20 September 2005 (UTC)
[edit] edit on 2006-6-13
The main changes are:
- Carefully separate the cases of sets of numbers and sets of reals. This is an experiment that may be useful on arithmetical hierarchy as well.
- Emphasize the fact that this is lightface (maybe more emphasis needed?)
- I rephrased the introduction. The anlytical hierarchy is not really about second order logic; it is about higher type languages such as Z_2 or type theory in first order logic. Every use I know of is in the context of first order ZFC or first order Z_2.
- Add a reference to Rogers' book. I plan to add more references.
