A record is primarily a thing that describes another thing by enumerating some of its properties. In a certain sense then a record is a set of properties of a thing, and a record can describe a mathematical set in various ways, like enumerating its members or some features shared by them, but a record is not a set in a strict sense for it can contain properties that are extrinsic to the described thing and thus not members of the set. The only way to see a record as a set would be to define it as an ordered set of typed expressions.
The format of a record neither is a class. Because in Unidatab a record can only have one format (like you can write a letter on a card or on a sheet but not on both at the same time) while a mathematical set can be member of several classes.
Similarly, a subdatabase is a format for which there is a recorded description.
So if one wanted to do some calculus with Unidatab, she could only do it by considering records as descriptions of sets or descriptions of classes but not formats as classes nor records as sets. Once granted these points however and relying on the tools provided by SQL, some framework of logical operations can be defined for a particular Unid base.