We developed scales to measure the domains of physician knowledge and beliefs about race and human genetic variation and physician's use of race in the domains of interpretation and clinical decision (see conceptual model).
These models solve the cardinality problem by restricting the domain X of interpretation, so that, in them, X is in a suitable sense isomorphic to the 'function space' XX.
For sets X and Y, let XY denote the set of functions whose domain is Y and with values in X. Intuitively, if X is the domain of an interpretation of λ-calculus, then X should be, in some sense, isomorphic to XX because the domain should be closed under abstraction (as well as application).
For the domain of the interpretation of the language fragment in which "is the same surman as" is the I-predicate can, in fact, be taken to consist of men, namely, to be a class containing exactly one representative man for each class of men with the same surname.
Or we might mean: what entities must be included in the domain of the interpretation of T in order for T to be true, whether or not those entities must be assigned to the variables of the sentences in T. When predicates of the theory express extrinsic properties, this difference matters.
