The use of lists in the study of undecidable problemsin automata theory

Many of the problems in automata theory are unsolvable and can be classified intodegrees of unsolvability by their relative difficulty. In this note, natural reference sets are presented which belong to the complete degrees at each level of the arithmetic hierarchy. Also, some questions regarding lists of recursively enumerable sets are considered. These results resolve some apparent peculiarities and provide simple methods of determining the degrees of unsolvability for several well-known problems and permit easy construction of natural problems with high degrees of unsolvability.