 (Note: The use of this unusual notation \(\phi \{x; y \mid \psi (x,y) \}\) in this one definition is meant to avoid the implication that a relation is interpreted as a set of ordered pairs, that would be represented by the contemporary notation \(\phi \{\langle x,y \rangle \mid \psi (x,y) \}\). The PM notation for propositional functions, as in \(\phi \hat{x}\) uses a caret over the variable where we would write \(\lambda x \phi(x)\). The PM notation for a class is \(\hat{x} \phi (x)\). A two-place propositional function is identified with variables also with carets: \(\phi (\hat{x} \hat{y})\) and the corresponding relation \(\hat{x} \hat{y} \phi (x,y)\). This notation does not identify relations as classes of ordered pairs, and that is how our blend of PM and contemporary notation in \(\phi \{x ; y \mid \psi (x,y) \}\) is to be taken.)