Wikiproofs:Set-theoretical definition of JHilbert concepts/Chapter 2

Kinds
In JHilbert, mathematical thought is rendered as several kinds of expressions. What kinds, exactly, occur, is user-defined. For example, a JHilbert module on ZFC set theory might need expressions for sets, classes and well-formed formulas, and thus define three kinds to that effect.

As there is no additional data attached to kinds, we may model the kinds permissible for an expression with a finite subset of the names, $$K\subseteq\mathcal{N}$$.

Sometimes, however, we may wish to unite several kinds, or subsume one kind under another. For example, if we want to apply the results of a JHilbert module dealing with group theory which has a kind for elements of a group to a more generic module dealing with ZFC set theory, we may want to subsume the group element kind of the first module under the set kind of the latter.