Talk:Analytical hierarchy

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)

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The other major problem with this page is the conflation of formulas and sets. Consider for example the following passage:

A ${\displaystyle \Sigma _{1}^{1}}$ formula is a formula of the form ${\displaystyle \exists X\phi }$, where X is now a predicate and ${\displaystyle \phi \in \Sigma _{0}^{1}}$, while a ${\displaystyle \Sigma _{1}^{1}}$ set is a set of the form

${\displaystyle \{x:(\exists y\in S)\ R(x,y)\}}$,

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)