Talk:Axiom of constructibility

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Low	This article has been rated as Low-priority on the project's priority scale.

Philosophy: Logic Low‑importance

This article is within the scope of WikiProject Philosophy, a collaborative effort to improve the coverage of content related to philosophy on Wikipedia. If you would like to support the project, please visit the project page, where you can get more details on how you can help, and where you can join the general discussion about philosophy content on Wikipedia.PhilosophyWikipedia:WikiProject PhilosophyTemplate:WikiProject PhilosophyPhilosophy articles

Low

This article has been rated as Low-importance on the project's importance scale.

Associated task forces:
/
	Logic

Text and/or other creative content from this version of Statements true in L was copied or moved into Axiom of constructibility with this edit on April 16, 2020. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists.

Simple non-measurable set[edit]

„and the existence of a simple (\Delta^1_2) non-measurable set of real numbers“
What is a simple non-measurable set? Simple set? Are you sure that it is independent of ZFC? (references?) --Chricho (talk) 15:03, 29 December 2010 (UTC)[reply]

The parenthetical phrase is the explanation: a "simple", i.e. Δ¹₂, non-measurable set. I agree it's not perfectly clear. I replaced with with "analytic". — Carl (CBM · talk) 15:24, 29 December 2010 (UTC)[reply]

"Analytic" is

\Sigma _{1}^{1}

. Did you mean "projective"? Or maybe "analytical" (a little-used term for "lightface projective")? --Trovatore (talk) 22:35, 29 December 2010 (UTC)[reply]

I meant analytical; the link went to the right place so I didn't think about it. Thanks, — Carl (CBM · talk) 00:07, 30 December 2010 (UTC)[reply]

Hmm, "analytical" is not a great word because of the potential for confusion with "analytic", and I don't think it's used much, probably partly because of the possible confusion and partly because the projective hierarchy is usually the more relevant one. I wonder if it wouldn't be better to say something like "a set of relatively low complexity". --Trovatore (talk) 01:38, 30 December 2010 (UTC)[reply]

Now there is a link, much nicer… --Chricho (talk) 10:13, 30 December 2010 (UTC)[reply]

I see "analytical" in computability theory as often as "projective". It just depends whether you start on the lightface side or the boldface side. I'm afraid that if we use any words like "simple" or "complexity" without a link to one of the hierarchies, it will just lead to the same confusion that "simple" did. Since the well-ordering is lightface, we might as well link to the analytical hierarchy. — Carl (CBM · talk) 13:32, 30 December 2010 (UTC)[reply]