On the Recursive Enumerability of Fixed-Point Combinators - Goldberg, Mayer (BRICS Report Series, 2005)
We show that the set of fixed-point combinators forms a recursively-enumerable subset of a larger set of terms we call non-standard fixed-point combinators. These terms are observationally equivalent to fixed-point combinators in any computable context, but the set of on-standard fixed-point combinators is not recursively enumerable.