# Tag for alternative set theories?

The 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).

Wouldn't it be better to have a separate tag for them?

I believe the chances of these questions being seen by their intended audience would increase significantly that way. The way things currently are, most of these questions end up being ignored or are not answered by the appropriate experts.

• I think that this could be a supplementary tag, like [non-classical-logic] is to [logic]. Or we widen the scope of [set-theory] to include alternative set theories. Or both, of course (although my first suggestion sort of subsumes the second). – Asaf Karagila Apr 17 '18 at 15:01
• I upvoted although I'm not sure what the best approach is, because the post brought to my attention the exclusive nature of the current tag. I'd have used it if were going to ask something about $\mathsf{NF}$. – hardmath Apr 17 '18 at 15:18
• @Asaf I rather we do not widen the scope of the current tag. – Andrés E. Caicedo Apr 17 '18 at 15:23
• I agree that widening the scope is a bit tricky. But it seems to me that the de facto scope already includes much of the alternative set theories related questions (e.g. ETCS related questions). Admittedly, not many of them exist, so a retagging effort is certainly doable. – Asaf Karagila Apr 17 '18 at 15:26
• This discussion is somewhat related but it discusses specifically NFU: Should we have a tag for the set theory NFU? This tag existed for a short period in the past, the question which had this tag are currently tagged (set-theory). – Martin Sleziak Apr 17 '18 at 16:42
• "The set-theory tag is explicitly about mathematics (and metamathematics) in the context of ZFC and its subsystems and extensions." Where is this mentioned? – quid Apr 17 '18 at 17:34
• @Martin: I noticed now that "a short period" was over a year... – Asaf Karagila Apr 18 '18 at 7:11
• While there may be other reasons to make a separate tag, I'm not sure that there would be that many people who would follow a new-foundations tag, say, but not follow set-theory. Lacking such a tag, they presumably are following set-theory. In the particular example given, the issue is more a non-classical logic than an alternative set theory, so an alternative set theory tag would not have helped much. "Dialetheist Set Theory" doesn't seem to be a term, but rather "naive set theory" in a dialetheist framework (a variant of paraconsistent logic) seems to be the intent. – Derek Elkins left SE Apr 19 '18 at 23:35
• I would say that Von Neumann–Bernays–Gödel set theory (NBG) is very similar to ZFC. If the proposed tag for alternative set theories is created, would NBG belong under this new tag? – Martin Sleziak Apr 22 '18 at 16:32
• @Martin I think theories like NBG, Morse-Kelley (MK), or Kripke-Platek (KP) are natural variants, extensions, or subsystems of ZFC. The situation with NFU is a bit curious in that significant work in the area has taken place by actually working in ZFC (with large cardinals) and then translating. – Andrés E. Caicedo Apr 22 '18 at 17:20
• Andrés E. Caicedo (and @AsafKaragila). I'd say that discussion so far indicates that prevalent opinion is in favor of new tag, but there is not much feedback on what to include. Would you be willing to write an answer with suggestion of possible tag-wiki - this would make the proposal of new tag more specific and also give a place for others to comment if they have suggestions what to include in the tag-info. (I think it is reasonable to do this while the post is less than 14 days old and it is still shown in the community bulletin.) – Martin Sleziak Apr 27 '18 at 4:48
• @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 Karagila May 5 '18 at 10:07
• @Asaf Ah, very good. I was still waiting for a moment to think carefully about the phrasing of the tag-info. – Andrés E. Caicedo May 5 '18 at 11:43
• @AndrésE.Caicedo Your comment suggests that you are planning to create tag-info. Since some time has passed and I did not want this to be completely forgotten, I have created at least very basic tag-info. Of course, feel free to rework it completely if you wish. (After all, you have suggested creation of the tag.) – Martin Sleziak May 27 '18 at 19:14
• @AsafKaragila and Andrés E.Caicedo: Do you think some of the set theories mentioned in Peter Smith's post Alternative set theories should be added to the tag-info (SP, ZFA, ECTS)? – Martin Sleziak May 28 '18 at 4:35

1. I am for creating the tag. Or some similar name, but a tag intended for the set theories suggested in the question. (Although probably some discussion would be needed about the exact scope of the new tag.) The consensus in the previous discussion about (nfu) tag was that this tag would be too specific. Having a common tag for several similar theories might be a reasonable compromise - instead of having several very specific tags with low usage we get a single umbrella tag, but still not too big. I agree with the suggestion in the question that this might improve chances that people who are interested (and knowledgeable) in these topics would have better way to follow (or at least find) such questions.

2. I think that questions about this topic should not be excluded from the tag. As far as I can tell, currently such question typically get the tag and I think it is quite reasonable, so I am for continuing this practice. (As far as I can tell, nothing in the current revision of the tag excerpt and the tag-wiki for (set-theory) says that such question do not belong there.)
I think it is useful if a question gets also relatively specific tag (if such tag exists) but also a tag from some big area (if there is such tag suitable for the question at hand). Specific tags are much better for filtering results for searching. Big tags usually have more followers and their improve the chances that the question gets to a wider audience.

3. We need a good tag-wiki. I think that it would be useful to list at least some of alternative set theories which belong here in the tag-info. (I leave to more knowledgeable users to suggest which ones, since I do not know much about this area. Other than NF and Vopěnka's AST I did not encounter such theories. Although my guess would be that probably some of the theories listed in the Wikipedia article Alternative set theory might fit here.)

4. Maybe some synonyms could be useful. If somebody asks a question about NFU (as an example), they might be unaware that the tag 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 $\to$ (alternative-set-theories), $\to$ (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.)

• Thank you for the thoughtful answer. – Andrés E. Caicedo Apr 22 '18 at 17:21
• The tag was created recently. – user99914 May 6 '18 at 5:50
• Since the tag was created, I will also ask: What you think about creation some synonyms as mentioned in point 4. – Martin Sleziak May 28 '18 at 2:44
• I am not sure about the synonyms. I still think NF and NFU are special enough that at some point we may want to revisit the issue and re-create a (new-foundations) tag instead. – Andrés E. Caicedo May 29 '18 at 13:36

It seems that there is a disagreement whether or not the new tag should be used in conjunction with or not. (This was explicitly mentioned in the original version of tag-excerpt and tag-wiki, but then edited away.)

Probably it might be useful to post a separate answer on this issue, so that it can be discussed (commented, voted up/down) separately.

Here are my arguments for using the new tag together with tag:

• Using also a bigger tag gives the question better chance to get noticed. Now the difference is simply because the tag is very new, but it seems quite likely that the tag (set-theory) will always have much more followers then (alternative-set-theories).
• As far as I can tell, the tag-info for (set-theory) never said that it is exclusively about ZF and ZFC. (In fact, even from comments by the OP it seems that he considers axiomatic theories such as NBG, MK, KP belong under (set-theory) tag rather than (alternative-set-theories) tag.) The OP explicitly says that intention behind creation of the new tag is that the questions from this area have better chance of getting noticed. Excluding the most important tag related to the topic works against this goal.
• Maybe the tag (nfu) can be considered as some kind of predecessor of this new tag. Although it only ever existed on three question, in all cases it was used together with set theory: 87171 (revision history), 193198 (revision history), 208818 (revision history).
• I thought that 11 upvotes on the other answer, which explicitly says that "questions about this topic should not be excluded from the set-theory tag" was sufficient evidence that this solution is preferred. (OTOH I have no problem to admit that the other answer contains 4 separate points, not every upvoter necessarily agreed with all of them. But I do not see any comments against this under that answer and if I look at comments under the question, they seem to be more in support of including (set-theory) tag.) – Martin Sleziak May 28 '18 at 2:42