I can imagine a reasonable question which could be tagged with the tags transfinite-induction, transfinite-recursion, ordinals, elementary-set-theory. Having only five spots for tags, this might become a problem at some point (at least for some questions.)
Transfinite induction and transfinite recursion are not the same, but these two topics are definitely close to each other. Basically the difference is that in one case we are proving some result by induction on ordinal numbers. In the other case we are proving existence of some object using this technique. (I have decided to be cautious and avoided using work "constructing" or "defining" some object, but for informal description they might sound better and make the distinction clearer.)
- Would it be better to have these two topics in the same tag? If we want to create one tag for both topics, what would be the name of the new tag? Or should we simply create synonym between the two tags in one direction?
- Should we use simply ordinals to tag questions about transfinite induction/recursion? If yes, then should there be a synonym from these two tags to the master tag (ordinals), or is it sufficient to remove the tags and explicitly mention in the tag-info for ordinals that the tag is intended also for these question?
- Or is the situation satisfactory as it is currently and it is better to keep two separate tags to make the distinction?