Talk:Scale (descriptive set theory)

Re-creating without copyvio

The previous version of this page was deleted in the grounds that it was a copyright violation. Re-writing without violating copyright.

There is a question here — I don't think at the moment that we have a good rationale for two separate articles, one on the scale property and the other on scales. So which article should we have? Possibly it would make sense to move this article to scale (descriptive set theory), parallel to prewellordering being the article and prewellordering property a redirect to it. I'm personally not sure; I invite arguments one way or the other. --Trovatore (talk) 04:17, 2 January 2010 (UTC)

Update: I decided scales are the more fundamental notion, and moved the article here. It is of interest to know about (definable) scales on a pointset of pointclass Γ even if the scale is of some greater complexity. --Trovatore (talk) 07:57, 13 September 2010 (UTC)

What to say about scale property => uniformization property?

What I had earlier written was too simple, though it does give you the right answer in the most obvious case ($\Delta _{2n}^{1}$ determinacy, which is what you need for the scale property for $\Pi _{2n+1}^{1}$, is also what you need for the uniformization property for $\Pi _{2n+1}^{1}$ and $\Sigma _{2n+2}^{1}$, and the proof goes through the scale property for $\Pi _{2n+1}^{1}$. But that doesn't seem to rule out the existence of a scaled pointclass (not closed under universal real quantification) that does not have the uniformization property, though I don't actually know of an example (does anyone?).

So how to summarize this so that it makes sense? In some sense the main point, or at least one of the main points, of scales, is to get uniformization. But apparently they don't quite go level-by-level in a way that can be summarized briefly. --Trovatore (talk) 09:58, 8 January 2010 (UTC)