Should we merge all three of them?
I looked at the questions with dbms, and all of them were about databases. Since I saw no one disagreeing with this part of the proposal, I went ahead with merging them and making dbms a synonym of databases
As for databases vs. database-theory, we could merge databases into database-theory without making a synonym. This means that all current questions tagged with databases will be retagged into database-theory, but since the tags are not synonyms, it is still possible to tag a question with databases without being part of database-theory.
However, it seems to me that as a tag, databases and database-theory provide about the same information about the question, and this is reflected in most of the questions in this tag. So I instead suggest to both merge and synonymize databases into database-theory, because this seems to reflects the usage of the tags the best. (maybe the tag description could also be updated...) I can go ahead and perform this merge once I see enough support (i.e. votes or comments) for this decision.