Characterization of the effective computability in $\mathfrak{f}$-enumerations

Abstract

The main definitions of $f$-basis, $f$-enumerations and $f$-admissibility are given. As a main result the equivalence between $f$-admissibility and prime compurability in $\mathfrak{n}$ is proved. Finally, three variants of the main theorem are proved. The first two ones are generalizations of the directions "$\Leftarrow$" and
"$\Rightarrow$" of the main theorem. In the third variant potentially $f$-admissible functions are concerned.