V. V. Verbovskiy, A. B. Dauletiyarova, “Piecewise monotonicity for unary functions in <nobr>$o$</nobr>-stable groups”, Algebra Logika, 2021, Volume 60, Number 1,Pages <nobr>23–38</nobr>

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Algebra Logika, 2021 Volume 60, Number 1, Pages 23–38 (Mi al2647)

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Piecewise monotonicity for unary functions in $o$-stable groups

V. V. Verbovskiy^ab, A. B. Dauletiyarova^cd

^a Kazakh National Technical University after K. I. Satpaev
^b Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan, Almaty
^c Kazakh-British Technical University
^d Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: Unary functions definable in $o$-stable ordered groups of nonvaluational type are studied. Such functions are proved to be piecewise monotone and continuous.

Keywords: $o$-stable groups, unary functions.

UDC: 510.67

Received: 21.03.2020
Revised: 31.05.2021

DOI: 10.33048/alglog.2021.60.102

English version: Algebra and Logic, 2021, 60:1, 15–25

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© Steklov Math. Inst. of RAS, 2026