Talk:Axiom of constructibility

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Simple non-measurable set

Latest comment: 13 years ago7 comments3 people in discussion

„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)

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)

"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)

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)

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)

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

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)

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