Abstract
Studying the properties of almost ω-categorical quite o-minimal theories, we prove that the arbitrary families of pairwise weakly orthogonal nonalgebraic 1-types in these theories are orthogonal. We also establish the binarity of these theories.
Similar content being viewed by others
References
Macpherson H. D., Marker D., and Steinhorn C., “Weakly o-minimal structures and real closed fields,” Trans. Amer. Math. Soc., vol. 352, no. 12, 5435–5483 (2000).
Baizhanov B. S., “Expansion of a model of a weakly o-minimal theory by a family of unary predicates,” J. Symb. Log., vol. 66, no. 3, 1382–1414 (2001).
Kulpeshov B. Sh., “The convexity rank and orthogonality in weakly o-minimal theories,” Izv. Nats. Akad. Nauk Resp. Kaz. Ser. Fiz.-Mat., vol. 227, no. 1, 26–31 (2003).
Ikeda K., Pillay A., and Tsuboi A., “On theories having three countable models,” Math. Logic Quart., vol. 44, no. 2, 161–166 (1998).
Sudoplatov S. V., Classification of Countable Models of Complete Theories. Parts 1 and 2 [Russian], Izdat. NGTU, Novosibirsk (2018).
Kulpeshov B. Sh. and Sudoplatov S. V., “Vaught’s conjecture for quite o-minimal theories,” Ann. Pure Appl. Logic, vol. 168, no. 1, 129–149 (2017).
Mayer L. L., “Vaught’s conjecture for o-minimal theories,” J. Symb. Log., vol. 53, no. 1, 146–159 (1988).
Emelyanov D. Yu., Kulpeshov B. Sh., and Sudoplatov S. V., “Algebras of distributions of binary isolating formulas for quite o-minimal theories,” Algebra and Logic, vol. 57, no. 6, 429–444 (2018).
Kulpeshov B. Sh., “Maximality of the countable spectrum in small quite o-minimal theories,” Algebra and Logic, vol. 58, no. 2, 137–143 (2019).
Kulpeshov B. Sh. and Sudoplatov S. V., “Linearly ordered theories which are nearly countably categorical,” Math. Notes, vol. 101, no. 3, 475–483 (2017).
Woodrow R. E., Theories with a Finite Number of Countable Models and a Small Language, Ph. D. Thes. Simon Fraser Univ. (1976).
Baizhanov B. S., “One-types in weakly o-minimal theories,” in: Proc. Informatics and Control Problems Institute, Informatics and Control Problems Inst., Almaty, 1996, 75–88.
Baizhanov B. S. and Kulpeshov B. Sh., “On behaviour of 2-formulas in weakly o-minimal theories,” in: Mathematical Logic in Asia, Proc. 9th Asian Logic Conf., World Sci., Singapore, 2006, 31–40.
Kulpeshov B. Sh., “Weakly o-minimal structures and some of their properties,” J. Symb. Log., vol. 63, no. 4, 1511–1528 (1998).
Kulpeshov B. Sh., “Countably categorical quite o-minimal theories,” J. Math. Sci., vol. 188, no. 4, 387–397 (2013).
Kulpeshov B. Sh., “Binary types in ℵ0-categorical weakly o-minimal theories,” Math. Logic Quart., vol. 57, no. 3, 246–255 (2011).
Author information
Authors and Affiliations
Corresponding authors
Additional information
To Academician Yu. L. Ershov’s 80th jubilee.
The authors were partially supported by the Ministry of Education and Science of the Republic of Kazakhstan (Grant AP05132546).
Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 3, pp. 484–498.
Rights and permissions
About this article
Cite this article
Altayeva, A.B., Kulpeshov, B.S. Binarity of Almost ω-Categorical Quite o-Minimal Theories. Sib Math J 61, 379–390 (2020). https://doi.org/10.1134/S0037446620030015
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446620030015