Talk:Cardinality

Merger proposal Infinite sets

I propose that Infinite set be merged into Cardinality#Infinite sets. I think that the content in the Infinite set article can easily be added to this page, as most of it is already on this page.

DrWikiWikiShuttle (talk) 06:35, 26 June 2016 (UTC)

Oppose: No. I do not think that its content is contained here, and it is important enough to deserve its own article. JRSpriggs (talk) 15:01, 26 June 2016 (UTC)

Oppose - This is a notable article, with a notable context. It should have an article of its own. ♥ Shri Sanam Kumar ♥ 17:55, 18 October 2016 (UTC)

(G)CH and research

Lurking through Jochen Burghardt's talk page, I happened upon a discussion that took place last November or so, where previous text had mentioned ongoing research into CH, which had been labeled with {{cn}}, then someone made the statement less specific and removed the template, then the whole thing got removed. Jochen wrote and edit summary that said restore ((cn)) after sentence that hasn't changed since it was added: I doubt that Cohen.1963 (independence of GCH) leaves much room for research, but I'm not an expert

So here's the thing: independence from ZFC does not close an issue in set theory. All sorts of set-theoretic research is into questions known to be independent of ZFC, and indeed specifically into the continuum hypothesis. It would be easy to supply citations for examples of such research. Finding a reliable secondary source for the specific statement that research continues into the continuum hypothesis would be harder, as this is at a more "meta" level, but I expect it can be done.

If we're going to continue to talk so much about CH in this article, I do think it's reasonable to mention continuing research efforts. It seems to me that it ought to make sense to cite specific research directions and cite those, rather than needing to find a secondary source for the "meta" statement; would others find this acceptable?

On the other hand, I'm not sure that the general article on cardinality needs to deep-dive into this at all. --Trovatore (talk) 20:07, 20 September 2023 (UTC)

@Willondon:, the other participant in the previous discussion. --Trovatore (talk) 20:22, 20 September 2023 (UTC)

Seems you're referring to my post at User talk:Jochen Burghardt#Continuing research on cardinality?. My closing opinion, "I thought (well, assumed, to be honest) that there were surely open questions still. Given that nobody (including 250 page watchers) has addressed the template with an actual citation, I thought it best to delete my essentially original research." That's still my opinion: that my opinion should be dismissed, because it relied on original research by assumption. I have no valid opinion on whether or not research is settled or continues. _signed, Willondon (talk) 21:03, 20 September 2023 (UTC)

Research does continue, and citations can be found. The real question is whether it makes sense to talk about it here (or indeed whether this article should talk so much about the cardinality of the continuum, when the article is about cardinality in general).

But then again, CH is sort of the first question that came up that wasn't immediately resolvable, so it might well make sense. --Trovatore (talk) 21:06, 20 September 2023 (UTC)