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Every computable set is generically reducible to every computable set that does not have density 0 or 1
The notion of generic reducibility was introduced by A.Rybalov in his CiE
2018 paper: a set A is generically reducible to set B if there exists a total
computable function f that m-reduces A to B such that the f-preimage of every
set that has density 0 has density 0. It may be considered as the ``generic
version'' of the notion of m-reducibility.
In this note we improve one of his results and show that every two computable
sets that do not have density 0 or 1 are equivalent with respect to generic
reducibility, and that every computable set is reducible to every computable
set that does not have density 0 or 1, thus providing a complete classification
of computable sets with respect to generic reducibility