On minimal numerations (Q1914753)

The author offers internal minimality criteria for a computable numeration which have recourse to the algorithmic description of its enumeration equivalence. As a consequence, the author gives a classification of the class of all minimal numerations. He also constructs a computable discrete family of recursively enumerable sets without computable enumerations and a family of recursively enumerable sets, all computable enumerations of which are minimal but not positive.