Added link to Dominik Kirst’s Coq formalization of Andrew Swan’s argument.

]]>Looks good to me.

]]>Have moved the section “History” to right before “References” and turned the section “Assessment” into a remark inside “Statement and proof”.

]]>Actually, the “assessment” is better placed where it is, I think. This is because, in “In constructive mathematics” we are actually discussing the topics of the “assessment”. Namely that classically two things are equivalent to choice, about which in “In constructive mathematics” we learn that one is constructively equivalent to choice but the other isn’t. So perhaps I would keep things as they are, but changing the title “assessment”. Maybe “discussion”? Not perfect but perhaps less worse than “assessment”?

]]>Go ahead if you want to do it. It seems that you have an editing plan in your head already.

]]>I agree. I found the “assessment” a bit odd, not in its contents, which is interesting, but in its title.

]]>By the way, I would re-structure that entry, regarding the material that was already there before you came in:

the section “Assessment” is hardly worth a section, this should be a

`\begin{remark} ... \end{remark}`

and I find even that is unnecessary, as that assessment is at best besides the point (famous as that quote may be)the section “History” should be moved down to right before the references, not to distract from genuine content

This way your material “In constructive mathematics” would be moved up to where it’s more relevant, and maybe it should be inside “statement and proof”.

]]>Oh, I see that you already did it. Good.

]]>Thanks, Urs, for both comments. I will add it later after I study the template.

]]>Following up on #16:

In fact we already have a page *John Lane Bell*, so best to link to it, too.

Removed “classically” at the beginning of the file, as this assumption is no longer needed.

]]>Removed “if one admits the principle of excluded middle” from the beginning of the page, an assumption which is no longer needed after Andrew Swan.

]]>How do I reference this reference in nLab syntax?

Following the template here I’d do something like this:

- J. L. Bell,
*Zorn’s lemma and complete Boolean algebras in intuitionistic type theories*, The Journal of Symbolic Logic, 62(4):1265–1279, 1997 (doi:10.2307/2275642)

Improved the reference to Bell.

]]>I’ve added a reference, by John Bell, that Zorn’s Lemma doesn’t imply excluded middle. How do I reference this reference in nLab syntax?

]]>Fixed Zorn’s lemma as well.

]]>Fixed an incorrect claim. The well-ordering principle is actually equivalent to the axiom of choice in constructive mathematics, as proved by Andrew Swan (and formalized in Agda by Tom de Jong).

]]>Thanks for the angle-bracket hint. Done!

]]>Hi Martin, thanks for picking this up.

PS If you want urls to turn into links, you need to surround them with angle brackets, like `<https://example.com>`

, and have the Markdown option selected, to get https://example.com

My student Tom de Jong formalized Swan’s answer in Agda, by the way (also taking into account a question I made after his answer).

]]>I asked the same question in the Zulip HoTT chat. Andrew Swan’s answer is that the (inductive) well-ordering principle implies excluded middle (and hence choice, I believe): https://hott.zulipchat.com/#narrow/stream/228519-general/topic/inductive.20well-ordering.20gives.20excluded.20middle.3F/near/246881801

]]>This page claims that the well-ordering principle doesn’t imply excluded middle. But the way the paragraph is written is a bit ambiguous, and it may be interpreted as saying that the well-ordering principle doesn’t *seem* to imply excluded middle. If the former, does anybody know a reference for this?

Removed old discussion in query box.

]]>Sure, the discussion can be removed.

]]>