 There are, of course, uncountably many subsets of the natural numbers. But for each such \(A \subseteq \mathbb{N}\), we may still understand \(\chi_A(x)\) as a new primitive functional symbol which can be employed in constructing one of countably many \(A\)-partial recursive definitions in the manner discussed in  Section 2.1.1. It is thus also possible to list off all of the unary \(A\)-partial recursive functions relative to the codes of their definitions to obtain a uniform enumeration 