Hmm... I have been playing with relational algebra, while reading C.J. Date's Introduction to Database Systems and Foundation for Future Database Systems. At the moment I don't remember how trees are implemented in a truly relational language, but apparently they are much better implemented in relational algebra than in the typical SQL "CONNECT BY".
You might try either of those books, or see if you can find some info on Fabian Pascal's Database Debunkings
When I have the time, I might look that syntax up and get back to you .
(One note: the "pure" relational algebra people say NULLs are a bad idea. And, in true formal logic, a NULL is unknown, thus you can't test it for equality with anything; you can only test if something IS or IS NOT NULL)