Should questions about Zorn's lemma be tagged (axiom-of-choice)?

Question

We have plenty of questions concerning Zorn's lemma and its applications. Some of them are tagged axiom-of-choice, 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 axiom-of-choice?

(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 axiom-of-choice 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.

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We know that ZL and AC are equivalent statements. So my take on this that a question which would be tagged axiom-of-choice if all occurrences of ZL in the question were replaced by AC, then it seems to be reasonable to tag this question by axiom-of-choice 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 axiom-of-choice 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 zorn-lemma tag? Or even equivalents-of-ac?

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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 axiom-of-choice instead.

Answer 1

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 intersection 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 set-theory, not all questions involving choice, even "indirectly" as in ZL, are axiom-of-choice. 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 axiom-of-choice 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 choice-principles 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.