The main result is that for sets
, the following are equivalent: (1)
The shuffle sum σ(S) is computable.
(2)
The set S is a limit infimum set, i.e., there is a total computable function g(x, t) such that
enumerates S.
(3)
The set S is a limitwise monotonic set relative to 0′, i.e., there is a total 0′-computable function \({\tilde{g}(x,
... [Show full abstract] t)}\) satisfying such that enumerates S.
Other results discuss the relationship between these sets and the sets.