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We have plenty of questions concerning Zorn's lemma and its applications. Some of them are tagged , some are not; for a sample you can have a look at results of this search.

Shouldn't most of questions about Zorn's lemma include the tag ?

(If some kind of consensus on this is reached, the clarification should be incorporated into the tag-excerpt and tag-wiki.)

EDIT: Since it seems that my formulation was rather unfortunate and might lead to confusion. When I write questions about Zorn's lemma, you should read this in the way such that questions about axiom of choice would mean questions deserving tag. (I have tried to expand more on this below.)

I have removed the phrase most of from my original formulation - as Asaf's answer shows, it seems as if my suggestion was something like: Whenever ZL appears in a question, this tag should be added. This was not what I intended to say.


We know that ZL and AC are equivalent statements. So my take on this that a question which would be tagged if all occurrences of ZL in the question were replaced by AC, then it seems to be reasonable to tag this question by as well. (Of course, replacing ZL by AC might render the question nonsensical, I just mean that in principle relevance of ZL to the question might grant using this tag if relevance of AC would.) In the past, I have added the tag to a few questions because ZL was very relevant to that question.

The same argument could apply to well-ordering principle, although I'd say we have less questions where WO is an important part of the question.

But maybe other users have different opinion; so I'd like to hear what MSE community thinks about it. Would it be better to have tag? Or even ?


FWIW there was a suggestion to have tag called (choice-principles) some time ago, see here. The way I understood it, it was meant for questions about weaker version of AC. But the tag was quickly removed and it was suggested to use instead.

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    $\begingroup$ If created, zorn-lemma should definitely be a synonym to axiom-of-choice $\endgroup$ – Willie Wong Sep 27 '13 at 8:32
  • $\begingroup$ chaos in tags usage is enough to impair tags usage policies. $\endgroup$ – user79193 Sep 28 '13 at 17:38
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I strongly disagree with the idea of adding such tag[s].

The axiom of choice tag is for questions which really have one of the forms:

  • Where does the axiom of choice plays a role?
  • Can we prove this without the axiom of choice?
  • How much of the axiom of choice is provable from this statement?

Questions about using ZL sometimes fit under this description, but sometimes not. But I feel that adding such tag would be like adding the tag to every question which involves intersections (on an unrelated note, I don't like that tag either).

Much like not all questions involving sets are , not all questions involving choice, even "indirectly" as in ZL, are . This can be seen as if I'm arguing in favor of a ZL tag, but in fact I am not. I think that questions which ask specifically why do you need to use ZL, should be tagged with the tag; and questions which discuss a completely other topic (e.g. maximal ideals) which involves Zorn, but do not ask specifically what happens when Zorn's lemma fails, or so, shouldn't have any tag related to Zorn or choice.

On a final note, the seems completely redundant to me, because the AC tag does not even contain 500 questions at this point (and the tag was proposed a year ago), so searching through it is not a horrible mission; moreover essentially a third of the questions under the AC tag, and indeed a lot of the AC research papers are essentially about choice principles and there's no real reason for separating the two.

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  • $\begingroup$ I was not saying that every question involving ZL should be tagged (axiom-of-choice). (But probably I did not manage to be clear enough.) I was saying that if the questions would be tagged with this tag if AC was used instead of ZL, would deserve this tag. So when you are saying: I think that questions which ask specifically ... Zorn or choice; it is saying more-or-less the same thing. $\endgroup$ – Martin Sleziak Sep 27 '13 at 5:52
  • $\begingroup$ To give some specific examples: When I look at some of the first results of the search I've linked to; for example this, this and this would deserve (axiom-of-choice) tag based on the criteria you suggested. $\endgroup$ – Martin Sleziak Sep 27 '13 at 5:59
  • $\begingroup$ Martin, yes those three examples should be tagged with the AC tag. $\endgroup$ – Asaf Karagila Sep 27 '13 at 6:02
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    $\begingroup$ Ok, so I take it that whether the AC tag belongs to the questions does not depend on whether the AC is used as AC or in the form ZL. (Although we might have a different threshold when a question already deserves this tag; but this was not the point of my question.) $\endgroup$ – Martin Sleziak Sep 27 '13 at 6:03

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