Utm theorem

In computability theory the utm theorem, or Universal Turing machine theorem, is a basic result about Gödel numberings of the set of computable functions. It affirms the existence of a computable universal function, which is capable of calculating any other computable function. The universal function is an abstract version of the universal turing machine, thus the name of the theorem.

Rogers equivalence theorem provides a characterization of the Gödel numbering of the computable functions in terms of the smn theorem and the utm theorem.