|
This article is cited in 2 scientific papers (total in 2 papers)
Rogers semilattices for families of equivalence relations in the Ershov hierarchy
N. A. Bazhenovab, B. S. Kalmurzaevc a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Al-Farabi Kazakh National University, Almaty, Kazakhstan
Abstract:
The paper studies Rogers semilattices for families of equivalence relations in the Ershov hierarchy. For an arbitrary notation $a$ of a nonzero computable ordinal, we consider $\Sigma^{-1}_a$-computable numberings of the family of all $\Sigma^{-1}_a$ equivalence relations. We show that this family has infinitely many pairwise incomparable Friedberg numberings and infinitely many pairwise incomparable positive undecidable numberings. We prove that the family of all c.e. equivalence relations has infinitely many pairwise incomparable minimal nonpositive numberings. Moreover, we show that there are infinitely many principal ideals without minimal numberings.
Keywords:
Rogers semilattice, Ershov hierarchy, equivalence relation, computable numbering, Friedberg numbering, minimal numbering, universal numbering, principal ideal.
Received: 13.06.2018 Revised: 13.06.2018 Accepted: 19.12.2018
Citation:
N. A. Bazhenov, B. S. Kalmurzaev, “Rogers semilattices for families of equivalence relations in the Ershov hierarchy”, Sibirsk. Mat. Zh., 60:2 (2019), 290–305; Siberian Math. J., 60:2 (2019), 223–234
Linking options:
https://www.mathnet.ru/eng/smj3076 https://www.mathnet.ru/eng/smj/v60/i2/p290
|
Statistics & downloads: |
Abstract page: | 245 | Full-text PDF : | 33 | References: | 34 | First page: | 2 |
|