It was found an useful criterion of minimal numberings which allowed to establish new methods of building computable minimal numberings and caused a natural classification of computable minimal numberings. Jointly with S. Goncharov, it was constructed an infinite family of c.e. sets such that the family contains the least set under inclusion and has one-element Rogers semilattice. Jointly with S. Goncharov and A. Sorbi, the properties of completions of arithmetical numberings were investigated as well as interconnections of complete and universal numberings were examined.
Main publications:
Badaev S. A., Goncharov S. S., Sorbi A.
Completeness and universality of arithmetical numberings // Computability and Models. Dortrecht: Kluwer Acad. Publ. Group, 2002.
Badaev S. A., Goncharov S. S. Theory of numberings: Open Problems // Contemp. Math., 2000, 257, 23–38.
Badaev S. A. On minimal enumerations // Siberian Adv. Math., 1992, 2(1), 1–30.
