# What is elementary set theory?

The and tags are often confused by users (assuming the question was set theoretic to begin with...)

Moreover, many of the questions other would not regard elementary, I might and vice versa.

So for future reference (also, it will be easier to write the tag wikis) - what is elementary in set theory?

• I think that the distinction should follow the usefulness of the tags. One can easily imagine that the groups interested in or capable of answering questions on De Morgan and questions on forcing are only very weakly correlated. Obviously, there will always be a grey area, and using both tags will lead to pale blue questions for discriminating users, but for grey area questions the choice of the OP can simply be left untouched as it is a way of deciding the level of the answers. – Phira May 12 '11 at 18:29

I asked a similar question before. I am not an expert, so quoted from Arturo:

"Elementary-set-theory" is used to tag questions like this, about the basic theory of sets. "Set theory" is used to tag the kinds of questions that people who work in set theory think about: cardinal arithmetic, cofinality, models, forcing, independence of axioms, etc. We're trying to make sure the (set-theory) tag is not used for elementary questions, which is what (elementary-set-theory) is for.

In other words, it says what is not in elementary set theory.

• However the question "why is the union of ordinals is an ordinal?" can be seen as both of the tags. – Asaf Karagila May 12 '11 at 18:09
• @Asaf: Yes; there will be overlaps. The problem was that originally, [set-theory] was being used for questions at the level of point-set-theory (why does intersection distribute over unions, is a relation that is transitive and symmetric necessarily reflexive, etc). Set theorist complained (justifiably so); of course, some questions will lie at the intersection of both, being at the "high end" of [elementary-set-theory] and at the "low end" of [set-theory] (much like some questions can justifiably be tagged both [elementary-number-theory] and [number-theory]). – Arturo Magidin May 12 '11 at 18:27
• I was one of the people who complained enough to get the tag implemented. Arturo's explanations match my memory too. Some intersection is fine; the idea is just to make searching more useful. Someone who wants to know why the composition of two injections is again injective is not likely to want to get questions about forcing in the same search, and vice versa. – Carl Mummert May 13 '11 at 0:47

I went ahead and edited the tag wikis for set theory and elementary set theory, but since I evidently don't have sufficient reputation, the system didn't accept my edits fully; they apparently need to be "peer reviewed". But if those users with sufficient reputation take a look and make whatever changes would be desirable, then we'll have somewhat more informative tag information in the tag wiki. (Please double check my proposed description of elementary-set-theory, since I may have missed the mark...)

• Done. I just added "For questions about" at the beginning of the [set-theory] tag, to keep it in line with other excerpts. – Arturo Magidin May 13 '11 at 3:27
• I edited them some as well. Unfortunately there is not room to list every topic; I tried to keep the flavor the same. – Carl Mummert May 13 '11 at 3:42
• @Carl, Joel, Arturo (who will not be pinged, sadly): Thanks! – Asaf Karagila May 13 '11 at 7:09
• @Arturo, @Carl, thanks very much! And perhaps we can add Venn Diagrams to the elementary-set-theory tag? Also, I've noticed that for some reason when I hover my mouse over the tag, I still see my old version, but when I click to edit, I see your new version. – JDH May 13 '11 at 11:09
• The only obstacle is that there is a character limit for the "excerpt" portion. I removed continuum hypothesis and replaced it with Venn diagrams. If you are seeing an old version when you hover, it sounds like a caching problem; clearing your browser cache may fix it. – Carl Mummert May 13 '11 at 11:43