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.
Biography
Graduated from Department of Mathematics Novosibirsk State University in 1971 (chair for algebra and mathematical logic). Ph. D. thesis was defended in 1978. D. Sci. thesis was defended in 1996. A list of my papers contains more than 60 titles. Jointly with prof. V. P. Dobritsa, I am leeding the Almaty research seminar on mathematical logic since 1982.
Team leader of the projects: INTAS-RFBR-97-139 "Computability and Models" and INTAS-00-499 "Computability in Hierarchies and Topological Spaces".
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.
S. A. Badaev, S. S. Goncharov, “Полурешётки Роджерса с наименьшим и наибольшим элементами в иерархии Ершова”, Algebra Logika, 61:3 (2022), 334–340
2021
2.
S. A. Badaev, B. S. Kalmurzaev, N. K. Mukash, M. Mustafa, “One-element rogers semilattices in the Ershov hierarchy”, Algebra Logika, 60:4 (2021), 433–437; Algebra and Logic, 60:4 (2021), 284–287
S. A. Badaev, B. S. Kalmurzayev, N. K. Mukash, A. A. Khamitova, “Special classes of positive preorders”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 1657–1666
S. A. Badaev, N. A. Bazhenov, B. S. Kalmurzaev, “The structure of computably enumerable preorder relations”, Algebra Logika, 59:3 (2020), 293–314; Algebra and Logic, 59:3 (2020), 201–215
S. A. Badaev, A. A. Issakhov, “Some absolute properties of $A$-computable numberings”, Algebra Logika, 57:4 (2018), 426–447; Algebra and Logic, 57:4 (2018), 275–288
S. A. Badaev, S. S. Goncharov, “Generalized computable universal numberings”, Algebra Logika, 53:5 (2014), 555–569; Algebra and Logic, 53:5 (2014), 355–364
K. Sh. Abeshev, S. A. Badaev, M. Mustafa, “Families without minimal numberings”, Algebra Logika, 53:4 (2014), 427–450; Algebra and Logic, 53:4 (2014), 271–286
S. A. Badaev, S. S. Goncharov, A. Sorbi, “Some remarks on completion of numberings”, Sibirsk. Mat. Zh., 49:5 (2008), 986–991; Siberian Math. J., 49:5 (2008), 780–783
S. A. Badaev, S. S. Goncharov, A. Sorbi, “Isomorphism types of Rogers semilattices for families from different levels of the arithmetical hierarchy”, Algebra Logika, 45:6 (2006), 637–654; Algebra and Logic, 45:6 (2006), 361–370
S. A. Badaev, S. S. Goncharov, A. Sorbi, “Elementary Theories for Rogers Semilattices”, Algebra Logika, 44:3 (2005), 261–268; Algebra and Logic, 44:3 (2006), 143–147
S. A. Badaev, S. Yu. Podzorov, “Minimal coverings in the Rogers semilattices of $\Sigma_n^0$-computable numberings”, Sibirsk. Mat. Zh., 43:4 (2002), 769–778; Siberian Math. J., 43:4 (2002), 616–622
S. A. Badaev, S. S. Goncharov, “Rogers Semilattices of Families of Arithmetic Sets”, Algebra Logika, 40:5 (2001), 507–522; Algebra and Logic, 40:5 (2001), 283–291
S. A. Badaev, “On cardinality of semilattices of enumerations of nondiscrete families”, Sibirsk. Mat. Zh., 34:5 (1993), 3–10; Siberian Math. J., 34:5 (1993), 795–800
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