D. Yu. Emel'yanov, B. Sh. Kulpeshov, S. V. Sudoplatov, “Algebras of distributions for binary formulas in countably categorical weakly <nobr>$o$</nobr>-minimal structures”, Algebra Logika, 2017, Volume 56, Number 1,Pages <nobr>20–54</nobr>

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Algebra Logika, 2017 Volume 56, Number 1, Pages 20–54 (Mi al777)

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Algebras of distributions for binary formulas in countably categorical weakly $o$-minimal structures

D. Yu. Emel'yanov^ab, B. Sh. Kulpeshov^cb, S. V. Sudoplatov^deab

^a Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia
^b Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science RK, ul. Pushkina 125, Alma-Ata, 050010 Kazakhstan
^c International Information Technologies University, Manas str. 34A/Zhandosov str. 8A, Alma-Ata, 050040 Kazakhstan
^d Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
^e Novosibirsk State Technical University, pr. Marksa 20, Novosibirsk, 630073 Russia

Abstract: Algebras of distributions for binary isolating formulas over a type for countably categorical weakly o-minimal theories are described, and the generalized commutative property of an algebra of distributions for binary isolating formulas over a pair of types for countably categorical weakly ominimal theories is characterized in terms of convexity rank.

Keywords: countably categorical weakly $o$-minimal theory, convexity rank, algebra of distributions for binary isolating formulas, generalized commutative monoid.

UDC: 510.67

Received: 03.04.2015

DOI: 10.17377/alglog.2017.56.102

English version: Algebra and Logic, 2017, 56:1, 13–36

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