h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I have been working for some time with a database that deliberately violates First Normal Form, in that it allows a number of levels of nesting. Any cell (intersection of row and column) can itself contain a "table". There are limitations to the number of levels of nesting (dimensions?) in this particular implementation. However, it is a much better fit with business models of data where, for example, all the order lines are in the same record as the order itself, so that all the information about that order is obtained with a single operation (and no joins).
The question occurred to me, though, whether such a database could actually qualify as "relational"; many of its detractors claim not, but I can't buy their arguments (which essentially are that it has to conform to 1NF, 2NF, 3NF and so on - the arguments of the vendors of databases that do, funnily enough).
Would it be reasonable, I thought, to allow for a database to qualify as "relational" if it can deliver all of the functionality specified in that branch of mathematics called "relational algebra". It seems to me that it is (reasonable), which then leads one to ask whether absolutely everything relational algebraic operation must be supported or, if not, which ones? (Of course, the other databases must pass/fail the same test in order to qualify as "relational".)

For anyone who's interested the database in question is UniVerse, from the IBM stable (since 2001). It had its genesis in 1984, before SQL was invented, and before the likes of Oracle, Sybase, Ingres and so on existed.