Testwiki:Reference desk/Archives/Mathematics/2018 May 29

{| width = "100%"

|- ! colspan="3" align="center" | Mathematics desk |- ! width="20%" align="left" | < May 28 ! width="25%" align="center"|<< Apr | May | Jun >> ! width="20%" align="right" |Current desk > |}

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

May 29

Is the proposition $\mathrm{\exists }x((\mathrm{\varnothing }\in x)\wedge (x\in x))$ decidable in ZF ?

ZF, including the Axiom of Regularity. HOTmag (talk) 18:56, 29 May 2018 (UTC)

Yes, the axiom of foundation (which some people call "regularity") implies that no set is an element of itself. --Trovatore (talk) 21:20, 29 May 2018 (UTC)

Thanx. BTW, not only "some people" (as you call them), but also our article Axiom of regularity. HOTmag (talk) 21:48, 29 May 2018 (UTC)

Unfortunately. --Trovatore (talk) 22:43, 29 May 2018 (UTC)

It seems like you dislike this name, and I wonder why... HOTmag (talk) 22:46, 29 May 2018 (UTC)

Oh, I could come up with reasons, I suppose, but it boils down to the fact that "foundation" is the more usual name in my experience, which of course is influenced by the particular set-theoretic subculture I worked in. --Trovatore (talk) 22:48, 29 May 2018 (UTC)