Abstract
We introduce some alternative definitions of the concept of computable automorphism of a set of natural numbers. We study their relationships and investigate whether some classes of sets having isomorphic groups of automorphisms coincide with other classes of sets usual in computability. Finally, we show that the classification of sets by these groups of automorphisms is nontrivial.
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Combarro, E.F. On Classifying Subsets of Natural Numbers by Their Computable Permutations. Siberian Mathematical Journal 45, 125–135 (2004). https://doi.org/10.1023/B:SIMJ.0000013017.38330.2b
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DOI: https://doi.org/10.1023/B:SIMJ.0000013017.38330.2b