Note on cardinality of Rogers semilattice in the Ershov hierarchy
Abstract
The paper is aimed to show that we can easily construct a family consisting of any given number of elements whose Rogers semilattice consists of one element.References
M.M. Arslanov Ershov hierarchy. Kazan, 2007. In Russian.
S.A. Badaev and T. Talasbaeva Computable numberings in the hierarchy of Ershov.In Proceedings of 9th Asian Logic Conference, Novosibirsk, August 2005, S.Goncharov (Novosibirsk), H.Ono (Tokyo), and R.Downey (Wellington)(eds.). World Scientic Publishers.2006, pp.17–30
L. Ershov A hierarchy of sets, I. Algebra and Logic, 7:47–73, 1968.
L. Ershov A hierarchy of sets, II. Algebra and Logic, 7:15–47, 1968.
L. Ershov A hierarchy of sets, III. Algebra and Logic, 9:34–51, 1970.
L. Ershov Theory of Numberings. Nauka, Moscow, 1977. In Russian.
S. Goncharov and A. Sorbi Generalized computable numerations and non-trivial Rogers semilattices. Algebra and Logic, 36(6):359–369, 1997.
S. Ospichev Computable family of
S.A. Badaev and T. Talasbaeva Computable numberings in the hierarchy of Ershov.In Proceedings of 9th Asian Logic Conference, Novosibirsk, August 2005, S.Goncharov (Novosibirsk), H.Ono (Tokyo), and R.Downey (Wellington)(eds.). World Scientic Publishers.2006, pp.17–30
L. Ershov A hierarchy of sets, I. Algebra and Logic, 7:47–73, 1968.
L. Ershov A hierarchy of sets, II. Algebra and Logic, 7:15–47, 1968.
L. Ershov A hierarchy of sets, III. Algebra and Logic, 9:34–51, 1970.
L. Ershov Theory of Numberings. Nauka, Moscow, 1977. In Russian.
S. Goncharov and A. Sorbi Generalized computable numerations and non-trivial Rogers semilattices. Algebra and Logic, 36(6):359–369, 1997.
S. Ospichev Computable family of
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