 Taking into account the equivalences between models of computation summarized in  Section 1.6,  it is also possible to formulate a version of  Theorem 2.3  for each of the models of computation mentioned there. For instance, in the case of the Turing Machine model \(\mathbf{T}\), the analogous version of the Normal Form Theorem can be used to show that there is a single  universal Turing machine (see entry on Turing machines)  \(U\) such that every partial recursive function \(f(\vec{x})\) corresponds to that computed by \(U(e,\vec{x})\) for some \(e \in \mathbb{N}\). Complete proofs of this sort were given by Turing (1937, sec. 6) for \(\mathbf{T}\), by Kleene (1936a, sec. 2) for the general recursive functions \(\mathbf{GR}\) (see also Kleene 1952, sec. 58), by Shoenfield (1967, ch. 7.4) for the class \(\mathbf{F}_{\mathsf{PA}}\) of functions representable in Peano Arithmetic, and by Cutland (1980, ch. 5) for the Unlimited Register Machine model \(\mathbf{U}\).