Talk:Axiom of constructibility

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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

„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]

I hope someone will make this article worth reading

Because an article that never states what the subject of the article is is not worth reading.

The article defines the Axiom of constructibility as the statement that "every set is constructible".

But without defining the word "constructible", this article becomes meaningless.

And it is a total evasion of responsibility to merely link this article to the article about constructible sets.

The definition of a constructible set is rather complicated. Repeating it in this article instead of simply referring to its statement in the article on the constructible universe would be wasteful. And it would invite confusion if an addition, correction or clarification were made in one of the two places but not in the other. JRSpriggs (talk) 16:39, 16 April 2025 (UTC)[reply]