Elias E Combarro Symmetry of the universal computable function: A study of its automorphisms, homomorphisms and isomorphic embeddings

A permutation / of the natural numbers will be an automorphism [1] of this predicate if

for all natural numbers and

for all natural numbers and that is, if

for all natural numbers and

way. That is, if

We

Thus, these automorphisms are changes of coordinates with respect to which the computations of the recursive functions are performed in exactly the same way as in the original model. In other words, these are the symmetric transformations which take into account the way the computable functions are actually computed.