Universal computable enumerations of finite classes of families of total functions

Abstract

© 2016, Allerton Press, Inc.In the paper we introduce the notion of a computable enumeration of a class of families. We prove a criteria for the existence of universal computable enumerations of finite classes of computable families of total functions. In particular, we show that there is a finite computable class of families of total functions without universal computable enumerations.