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As the title suggests, I think we can merge those two tags. This site is not extremely prosperous with set theoretic questions, even less with those relating to large cardinals which are usually more advanced - so it might not get asked around here at all (I know that I tend to prefer MO for most of the large cardinals questions that I can't get answer in my local department)

Edit: After inspecting both the questions tagged under large-cardinals I can clearly say that neither is even on-topic.

(Seeing how I'm not familiar with the whole "background work" of MSE, I figured I should just post it here, any edits/retags/remarks or whatever are most welcomed)

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    $\begingroup$ What's wrong with keeping a descriptive, non-redundant tag? $\endgroup$ – Qiaochu Yuan Dec 15 '10 at 21:24
  • $\begingroup$ @Qiaochu: I think that the amount of questions about large cardinals on MSE is not large enough to keep a separate tag. $\endgroup$ – Asaf Karagila Dec 15 '10 at 21:26
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    $\begingroup$ @Asaf: tags are not only for organizing existing questions but for organizing future questions. Any tag that is descriptive and non-redundant will help people find questions that they are interested in, and therefore is useful. $\endgroup$ – Qiaochu Yuan Dec 15 '10 at 21:32
  • $\begingroup$ @Qiaochu: I agree, however as the current situation demonstrates most people just use the general [set-theory] tag, and those who do use [large-cardinals] are usually mistag it anyway. I said it in both my previous comment as well as my original post: I'm not sure how many questions actually involving large-cardinals are there going to be. In fact, I'm fairly certain that out of 78 questions tagged [set-theory] only four or five (three of which are mine) seem to be about large cardinals. I don't see how that is going to change significantly enough for a separate tag. $\endgroup$ – Asaf Karagila Dec 15 '10 at 21:44
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    $\begingroup$ Questions not from set theorists, if they involve any cardinals, would most often be about inaccessible cardinals, measurable cardinals, or large cardinals. What are the tags for those now and in case of a merging? $\endgroup$ – T.. Dec 15 '10 at 22:34
  • $\begingroup$ I have to agree with Qiaochu, why bother messing with the tags when you can just appropriately retag the questions? There is no reason to fix something that isn't broken, especially when that "fix" might harm something in the future. In fact what is broken isn't even the tags, it is the way the questions are tagged, so lets just retag them. $\endgroup$ – Sean Tilson Dec 16 '10 at 3:36
  • $\begingroup$ @T..: At the moment non-set theorists usually post under set-theory or elementary-set-theory, or completely misuse the large-cardinal tag (e.g. the current questions tagged under it). While I completely agree that there should be tags for specialized topics, I completely disagree with opening one for every topic. Especially for things that could just as well be embedded naturally into an existing tag, and won't attract too many questions to begin with - and thus creating confusion for people posting questions and unsure of the tag usage. $\endgroup$ – Asaf Karagila Dec 16 '10 at 7:48
  • $\begingroup$ MathOverflow has only a [large-cardinals] tag, by the way, not [cardinals]. $\endgroup$ – T.. Dec 16 '10 at 8:26
  • $\begingroup$ @T..: I don't think that elementary questions about cardinals are very common on MO, while the whole point I'm trying to make is that the questions about large cardinals are not very common in here. MO has no precalculus related tags either, while MSE does. $\endgroup$ – Asaf Karagila Dec 16 '10 at 10:34
  • $\begingroup$ For what is worth, I think it is a terrible idea to merge these two tags. If tidiness is really an issue, "cardinals" could be merged with "set theory". However, "large cardinals" is something specific. If a user mistakenly tags something inappropriately, we can always retag and leave a comment. There are quite a few questions in MO about large cardinals/set theory that would have been much more appropriate here (several were asked before MSE existed). It is possible that in the future more and more of these questions will be here, and the tags may prove useful. $\endgroup$ – Andrés E. Caicedo Dec 16 '10 at 21:00
  • $\begingroup$ I think the arguments for [cardinals] actually point to a [cardinality] tag, or no tag at all if the latter is considered essentially the same as [set theory]. $\endgroup$ – T.. Dec 16 '10 at 22:16
  • $\begingroup$ I'm not in favour of merging [cardinals] (and/or [large-cardinals]) into [set-theory], the whole point of the tags is to be able and browse easily and find several topics. The way I see it [set-theory] should be more or less an umbrella tag, to keep in the "interesting tags" list, but [cardinals] (or whatever) should be the specific one to help you focus your search. The point is that you don't want a "discrete" topology of tags, not every question or small-enough-on-MSE topic should have a separate tag. I think that [large-cardinals] is a fine example for that. $\endgroup$ – Asaf Karagila Dec 16 '10 at 23:35
  • $\begingroup$ @T..: My argument of Andres'? At any rate, [cardinality] is plain wrong in my opinion because it seems (at least in my eyes) very far from cardinals related questions. I mean, even though cardinals are dealing with sizes of sets, essentially large-cardinals are dealing with consistency, and general cardinals are more about infinite arithmetic than just plain enumerations. $\endgroup$ – Asaf Karagila Dec 16 '10 at 23:37
  • $\begingroup$ @asaf: some of the "large cardinals" questions here were about basic properties of the Aleph and Beth hierarchies, i.e., "large cardinalities" in the sense of sets bigger than the continuum. [uncountable-sets] or [powerset] would be comparable in meaning but -- if there is to be any additional tag at all beyond [set-theory] -- the simplest and most general seems to be [cardinality]. Also, [ordinals] may be useful, I don't know if it exists (yes, having it supports "cardinals" to some extent, but not enough to overcome the confusion with large cardinals). $\endgroup$ – T.. Dec 17 '10 at 6:07

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