Let \phi\colon \mathbb{N} \to \mathbf{P}^{(1)} be an admissible numbering of the computable functions; a map from the natural numbers to the class \mathbf{P}^{(1)} of unary (partial) computable functions.
We identify each property that a computable function may have with the subset of \mathbf{P}^{(1)} consisting of the functions with that property.