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There is no enumerability.
The equivalence of semidecidability and enumerability can be obtained by the technique of dovetailing.
(since completeness implies recursive enumerability)
It is an open question to give supports for a Church thesis for fuzzy mathematics the proposed notion of recursive enumerability for fuzzy subsets is the adequate one.
It was the development of computability theory (also known as recursion theory) that provided a precise explication of the intutitive notion of algorithmic computability, thus making the notion of recursive enumerability perfectly rigorous.
These words of mine may make poor philosophizing, but that cannot be said of my proofs of the linguistic genesis of mathematical concepts, of the fact, in other words, that those concepts arose neither from the enumerability of things nor from the cleverness of reason.
