I added the combinatorics tag to that question. It might not be a perfect one, but IMO this isl better than having no subject tags. And hopefully some users following the combinatorics tag can provide a better judgement (and retagging it), just like what Asaf and Andres having been doing for set theory tag.
@MartinSleziak a problem with all this synonymising is that I feel it is a half-way thing and because of this many users are a bit too generous with it. While this might not be clear from my comments I am actually more inclined to keep the tags in this case. (Except maybe in the semi-group case as it's a bit rare.) It's pretty unclear why it is desirable to strip the information in the more specific tag. The tag group-theory is pretty large.
Related to this, just recently somebody proposed all kinds of syns around inequalities. What do you think about those?
Why in the world is natural-numbers a synonym of elementary-number-theory?
It seems group or groups is neither a tag nor a syn.
Since you say you're for keeping tags ring-homomorphism and ring-isomorphism and similar - maybe it would be reasonable to post an answer with this suggestion on meta.
So far the only positively voted answer is the one suggested synonyms. By having answer with other possibilities we would at least see from votes and comments what other users think about it.
I suggest removing natural-numbers as a synonym for elementary-number-theory. I would favor natural-numbers as an own tag. But I am not sure whether this would result in a tag with two big use cases in wildly different areas. So I would like to discuss this.
Not every question about natural numb...
I guess it might be good to make some short list of tags which are often used incorrectly. In case they are some volunteers willing to watch them and retag questions where they are used incorrectly.
In any case, the reason why I talked about the synonyms a few days ago is to show that there are at least some benefits to such synonyms. (My points 1 and 2 there.) I'll leave judging whether the problems outweight the possible benefits for others.
Of course, if there is a tag which should be kept, then all this is a moot point - what I mentioned there is related to situations asking whether it is better to remove tag or to make it a synonym.
Now that natural-numbers is a separate new tag again, should we bring up on meta discussion what exactly belongs there? Maybe it would be better to make a single post about other similar tags - rational-numbers, real-numbers.
@MartinSleziak, I consulted the discussion you linked and found a valid objection by user quid who pointed out that one of the questions included under the tag was a technical algebra question not related specifically to Bourbaki. I agree with quid that the inclusion of that question under the tag "bourbaki" is inappropriate. On the other hand, there is a recognizable bourbaki approach to the philosophy of foundations, and a number of questions here are specifically on that topic. It is actually difficult to find those questions by searching "bourbaki" precisely for the reason user quid... — Mikhail Katz2 hours ago
...pointed out, namely, that many questions mentioning "bourbaki" are technical mathematical questions unrelated to bourbaki foundational views specifically. That's why such a tag would be useful. Note that there is an MO tag for bourbaki: mathoverflow.net/questions/tagged/bourbaki, somewhat along the lines I am suggesting. — Mikhail Katz2 hours ago
@MikhailKatz Clearly (based on your comments and also your attempt to create the tag) you are in favor of (bourbaki) tag, why not making a post on meta about this - as suggested by Jyrki Lahtonen. Your arguments why the tag might be useful would be seen by more users there than in this comment thread. In any case, since the several comments hare are related more to creating tags than to the actual question, I would suggest to continue this discussion in chat. (Or on meta, if you make a post about the new tag.) — Martin Sleziak11 secs ago