 According to the terminology Gödel would later introduce in (1934), in such a case \(\varphi_R(x_1,\ldots,x_n)\) represents \(R(x_1,\ldots,x_n)\). In this presentation, he also generalized his prior definition to say that a function \(f(x_1,\ldots,x_n)\) is representable in \(\mathsf{P}\) just in case there exists a formula \(\varphi_f(x_1,\ldots,x_k,y)\) such that for all \(n_1,\ldots,x_k,m \in \mathbb{N}\), 