Abstract
In the paper we study the maximal and minimal objects under Σ-reducibility of the families of the form {ℕ ↾ n: n ∈ A}.
This is a preview of subscription content,
to check access.Similar content being viewed by others
References
W. Calvert, D. Cenzer, V. Harizanov, and A. Morozov, Ann. Pure Appl. Logic 141, 61 (2006).
Yu. L. Ershov, Definability and Computability (Sib. School Alg. Log., Nauch. Kniga, Novosibirsk, 1996) [In Russian].
Yu. L. Ershov, “Σ-Definability of algebraic structures”, in Handbook of Recursive Mathematics (Elsever, 1998), Vol. 1, p. 235.
I. Sh. Kalimullin and M. Kh. Faizrahmanov, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 154(2), 107 (2012) [In Russian].
I. Sh. Kalimullin and V. G. Puzarenko, Algebra i Logika 48(1), 31 (2009).
I. Sh. Kalimullin and D. Kh. Zainetdinov, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 156(1), 22 (2014) [In Russian].
N. G. Khisamiev, Izv. Akad. Nauk Kaz. SSR Ser. Fiz.-Mat. 98, 51 (1981) [In Russian].
N. G. Khisamiev, Sibirsk. Mat. Zh. 29(6), 144 (1988) [In Russian].
N. G. Khisamiev, “Constructive abelian groups”, in Handbook of Recursive Mathematics (Elsever, 1998), Vol. 2, p. 1177.
B. Khoussainov, A. Nies, and R. Shore, Notre Dame J. Formal Logic 38(2), 165 (1997).
H. Rogers, Theory of Recursive Functions and Effective Computability (McGraw-Hill, New York, 1967).
Author information
Authors and Affiliations
Corresponding author
Additional information
(Submitted by M. M. Arslanov)
Rights and permissions
About this article
Cite this article
Faizrahmanov, M., Kalimullin, I. & Zainetdinov, D. Maximality and minimality under limitwise monotonic reducibility. Lobachevskii J Math 35, 333–338 (2014). https://doi.org/10.1134/S1995080214040155
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080214040155