Definability via partial enumerations with semicomputable codomains - Nikolova, Stela (Ann. Sofia Univ. Fac. Math. and Inf., 2000)
Let A be a total abstract structure. We prove that if a set A |A|^n is admissible in every partial enumeration of A with semicomputable codomain, then A is semicomputable in A in the sense of Friedman - Shepherdson.