A NOTE ON JOINS AND MEETS FOR POSITIVE LINEAR PREORDERS
Bazhenov N. Kalmurzayev B. Zubkov M.
2023Sobolev Institute of Mathematics
Siberian Electronic Mathematical Reports
2023#20Issue 11 - 16 pp.
A positive preorder R is linear if the corresponding quotient poset is linearly ordered. Following the recent advances in the studies of positive preorders, the paper investigates the degree structure Celps of positive linear preorders under computable reducibility. We prove that if a positive linear preorder L is non-universal and the quotient poset of L is infinite, then L is a part of an infinite antichain inside Celps. For a pair L,R from Celps, we obtain sufficient conditions for when the pair has neither join, nor meet (with respect to computable reducibility). We give an example of a pair from Celps that has a meet. Inside the substructure Ω of Celps containing only computable linear orders of order-type ω, we build a pair that has a join inside Ω
computable reducibility , computably enumerable preorder , positive linear preorder
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Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, Novosibirsk, 630090, Russian Federation
Kazakh-British Technical University, 59 Tole bi St., Almaty, 050000, Kazakhstan
Al-Farabi Kazakh National University, 71 Al Farabi Avenue, Almaty, 050040, Kazakhstan
Kazan (Volga Region) Federal University, 35 Kremlevskaya St., Kazan, 420008, Russian Federation
Sobolev Institute of Mathematics
Kazakh-British Technical University
Al-Farabi Kazakh National University
Kazan (Volga Region) Federal University
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