Definition 2.1.12 (lambda-definability). A partial function $f:{\mathbb{N}}^k\to \mathbb{N}$ is $\lambda$-definable if there is a $\lambda$-term $F$ such that $F{c}_{n_1}\dots c_{n_k}{\equiv }_{\beta }{c}_{f(n_1,\dots ,n_k)}$.