Admissible functionals in abstract structures with arbitrary power

Abstract

A way for generalizing the notion of admissible (or \flip{$A$} -recursive [2]) function for the case of arbitrary (not only denumerable) abstract structure is considered. For this purpose a notion of admissible functional is introduced and studied in the paper. Using this notion, a concept of admissibility for partial multiple valued function over arbitrary structure is introduced. It is established that a function is admissible if and only if it is absolutely search computable.