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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.
Let be an enumeration of Gödel numbers of computable functions. Then the partial function
is called the universal function.