Should there be a separate tag for partially ordered sets?

Question

Users who are on this site some time might have noticed that a separate tag for posets has been created and removed a few times in the past.¹

Certainly, partial orders are quite an important topic. On the other hand, there already is the tag order-theory which is suitable for questions about partial orders.² So by creating one additional tag we would not gain too much and we would use already two of the five possible slots for tags on such questions - since they would be typically tagged by this specific tag and also by (order-theory).

So my main questions are:

1. Should there be a separate tag for partial orders? Would such tag be actually useful?
2. If the consensus is that we do not want a separate tag for this purpose, would creating synonyms posets $\to$ order-theory, partial-orders $\to$ order-theory, etc., be useful?

The intention of the synonyms suggested in the second point is that new users might be unaware that order-theory is the tag suitable for questions about partial orders, so they might be looking for a tag with "poset" or "partial order" in the name. (As witnessed by repeated creation of such tags in the past.)³

If we compare the situation with MathOverflow, they have separate tags posets (198 questions) and order-theory (378 questions). If we look at those tags, there are 87 questions which have both tags and it seems that there is a fair share of questions which are about partial orders but do not have (posets) tag. So I am not sure whether separation into two tags contributes to having the site better organized on that site. This was discussed briefly also on Mathoverflow Meta, although the discussion there seems to be inconclusive: Two tags for partially ordered sets.⁴ (And, needless to say, the two sites are not exactly the same - so not everything that works there would also work here and vice versa.)

I would suggest to keep this discussion specifically about partial orders. I do not know about attempts to create a tags for linear orders (total orders) in the past - but if the need arises we can start a separate discussion about such tag. There already exists a separate discussion about well-orderings - and moreover well-orders seem to me sufficiently different from partial orders, so it's probably better not to discuss them in the same topic.

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¹For example, the tag posets was created recently in December 2017 - including tag-excerpt and tag-info. Shortly after removal by a moderator, the tag reappeared in January 2018 - including a new tag-excerpt and tag-info. Using the query from this post you can find several past occurrences of posets, poset and partial order. For example, the tag poset was created and removed in 2013, 2014, 2015 and 2018.

²The current revision of the tag-excerpt says: "Order theory deals with properties of orders, usually partial orders or quasi orders but not only those. Questions about properties of orders, general or particular, may fit into this category, as well as questions about properties of subsets and elements of an ordered set."

³To some extent in the spirit of this older discussion: Tags as redirects for correct tags. (Although the idea suggested there seems to be abandoned.)

⁴Looking at that discussion reminded me that there is a possibility that some users might mistakenly use this for order of a group. (Typically if a user does not read the tag-excerpt and decides only based on the name of the tag.) If you look at the 75 questions tagged order-theory+group-theory, many of them are mistagged. However, this is only tangentially related to this discussion.

Answer 1

I guess since I've been the only one to weigh in, I'll do so "formally" in an answer.

• I think creating synonyms posets $\to$ order-theory and partial-orders $\to$ order-theory will help users tag questions related to orders.

Synonyms are pretty cheap to create, and don't have the same downsides as creating too many tags, right? I personally didn't really know "order theory" was a subject in its own right, before seeing the tag here (and thus wouldn't have searched for it / tried to apply the tag to any questions I may have had about partial orders).

• I personally think synonyms are enough, and that we don't need a separate tag for partially ordered sets.

I suspect (but have no evidence to support my suspicion) that a significant portion, if not a clear majority, of questions tagged with order-theory deal with partial orders, and not something less stringent like a preorder (although the more specialized topic of lattice-orders has been relatively popular, with 821 questions using the tag at the time of writing). Thus, I suspect that splitting off questions about partial orders would leave the tag order-theory significantly less used, and it's not terribly popular to begin with.

My personal feelings are that the topic is not as popular as e.g. group-theory where significant tag specialization is necessary, nor does there seem to be a need to split questions about "genuine" order theory from those of a more elementary nature (as with the splits in our set-theory or number-theory tags and their elementary versions). But, I would especially welcome dissenting opinions here.

• I think order-theory should stay the master tag.

While there is potential for misusing order-theory for, e.g., the concept of "order" in group theory, a more specialized tag like partial-orders isn't a good fit for all questions pertaining to more general types of orders. I do think the current name is most appropriate for the master tag.