I'm note sure that this is the place in which to suggest that a tag be deleted, but: the (polish-notation) tag seems kind of useless (there are only 28 questions with the tag). It also lacks a tag description and wiki (or does at the time of this posting---I just suggested edits to both), which caused some confusion here.
@XanderHenderson I can imagine that this tag might be useful. Probably it would be good to see what other users think about the tag. So posting the suggestion to remove tag in the tag management thread might be a reasonable way to go. (Of course, you can wait a bit to see whether somebody posts some feedback here.)
Is it consistent with NBG-Pairing+PairUnion that $\omega$ is a successor ordinal?
Pairing is the axiom of NBG that says $\forall_{x,y} \exists_z (z=\{x,y\})$.
PairUnion I'll define as $\forall_{x,y} \exists_z (z = x \cup y)$.
The lower-case variable names here mean that all variables are sets....
The set-theory tag is explicitly about mathematics (and metamathematics) in the context of $\mathsf{ZFC}$ and its subsystems and extensions.
Every now and then we see questions about other set theories ($\mathsf{NF}$ is popular enough, but there are other versions, see here, for instance).
...
@Martin and Andrés, the tag has been recently created. I don't know if "the jury is still out" or not, so I wasn't sure what action is to be taken. — Asaf Karagila2 days ago
@Asaf Ah, very good. I was still waiting for a moment to think carefully about the phrasing of the tag-info. — Andrés E. Caicedo2 days ago
I have also suggested that if the tag is created, some synonyms might be reasonable.
> Maybe some synonyms could be useful. If somebody asks a question about NFU (as an example), they might be unaware that the tag alternative-set-theories exists on this site and that it is intended for questions about NFU.
> I suppose at least for the most common topics which belong under the proposed tag, it might be useful to add synonyms with this tag as the master tag (for example nfu $\to$ (alternative-set-theories), new-foundations $\to$ (alternative-set-theories), etc.) By this we achieve that if somebody asks a question from this topic, they find the tag if they type something like "new-foundations" or "nfu" in the tag field.
> (I am aware that there are many users who try to help with tagging new questions and include the tags which the OP missed. And this is especially true about posts related to set theory. But still, if we can make discovering the tag easier for the OP, I think we should do it.)
The set-theory tag is explicitly about mathematics (and metamathematics) in the context of $\mathsf{ZFC}$ and its subsystems and extensions.
Every now and then we see questions about other set theories ($\mathsf{NF}$ is popular enough, but there are other versions, see here, for instance).
...
