Remark 3

By abuse of language, in the theory of sets $\mathscr{T}$, the giving of $n$ distinct letters $x_1, \ldots, x_n$ (with no typical characterization and no axiom) is considered as a species of structure $\Sigma_0$, called the structure of a set on the $n$ principal base sets $x_1, \ldots, x_n$.