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There's really no appropriate tag for this question I just asked. One idea for labelling this question and other, similar questions, would be to create a new tag called "ordered algebraic structures." The synopsis could explain that this is meant to encompass partial order relations, not just linear orders.

If we create this tag, it would perhaps be wise to merge "ordered groups" and/or "ordered fields" so that now they're all just tagged "ordered algebraic structures."

What do you guys think?

  1. Should there be an "ordered algebraic structures" tag?
  2. Should this replace "ordered groups"?
  3. Should this replace "ordered fields"?

Related.

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  • $\begingroup$ Would simply tagging such a question as (for example) abstract-algebra, ring-theory and order-theory be okay? I would think so. $\endgroup$ – Najib Idrissi Mar 24 '15 at 16:52
  • $\begingroup$ @NajibIdrissi, woah there's a ring theory tag? I thought "commutative algebra" was all we had... Edit. I think the tag "order-theory" would be inappropriate in this case. The question really has nothing to do with order theory. It doesn't ask about least elements, joins, adjunctions, or anything else that is "order-theory-ish". $\endgroup$ – goblin Mar 24 '15 at 16:54
  • $\begingroup$ @NajibIdrissi, I also kind of think "abstract algebra" is a bit of a bad fit here (just removed it as a tag.) "Algebra" to me suggests that we're dealing only with functions and identities. But perhaps I am misunderstanding the connotations of that tag. $\endgroup$ – goblin Mar 24 '15 at 16:59
  • $\begingroup$ While I'm a bit iffy about order-theory, I completely disagree with that second comment about abstract-algebra... From the tag excerpt: "Abstract algebra is the study of algebraic objects. Some of the more common algebraic objects are groups, rings, fields, vector spaces, modules, and other advanced topics." Why would it not apply here? I don't understand to be honest. For example the Wikipedia page for "ordered group" literally starts with "In abstract algebra, ..." $\endgroup$ – Najib Idrissi Mar 24 '15 at 17:01
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    $\begingroup$ @NajibIdrissi, sorry, let me try to post a more sensible comment. (Second times a charm!) Algebra to me tends to suggest "objects are sets equipped with $n$-ary operations; arrows are homomorphisms; these things form a category." More generally, sometimes we have a fixed indexed set $J$; objects consist of a set $X_i$ for each $i \in J$, together with functions between Cartesian products of the sets, e.g. $X_1 \times X_2 \rightarrow X_2$. This doesn't encompass order relations, though. $$\;$$ Once again, let me emphasize that I fully admit that I may be understanding that tag too rigidly. $\endgroup$ – goblin Mar 24 '15 at 17:20
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    $\begingroup$ I think of ordered fields as special, and would prefer that that particular tag not disappear. $\endgroup$ – André Nicolas Mar 24 '15 at 17:36
  • $\begingroup$ If such a tag was created, I don't think it should replace the current tags. I can easily imagine someone following just one of those tags, and not really knowing much about or caring about the other. Also, I think that ordered-structures sounds better, and then pairing that with the relevant tag the describes the structure (like ring-theory) seems like a better solution to me. Although maybe that would have to much in common with order-theory tag $\endgroup$ – Paul Plummer Mar 24 '15 at 19:43

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