Abstract
Studying the properties of almost \( \omega \)-categorical weakly \( o \)-minimal theories of convexity rank 1, we prove the orthogonality of every family of pairwise weakly orthogonal nonalgebraic 1-types in the theories. Also, we establish the binarity of the theories.
This is a preview of subscription content, log in via an institution to check access.
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 [Russian]. Parts 1 and 2, Izdat. NGTU, Novosibirsk (2018).
Peretyatkin M. G., “Theories with three countable models,” Algebra and Logic, vol. 19, no. 2, 139–147 (1980).
Baizhanov B. S., “One-types in weakly \( o \)-minimal theories,” in: Proc. Informatics and Control Problems Institute, Informatics Control Probl. Inst., Almaty (1996), 75–88.
Altayeva A. B. and Kulpeshov B. Sh., “Binarity of almost \( \omega \)-categorical quite \( o \)-minimal theories,” Sib. Math. J., vol. 61, no. 3, 379–390 (2020).
Woodrow R. E., Theories with a Finite Number of Countable Models and a Small Language. Ph.D. Thesis, Simon Fraser University, Burnaby (1976).
Kulpeshov B. Sh. and Sudoplatov S. V., “Linearly ordered theories which are nearly countably categorical,” Math. Notes, vol. 101, no. 3, 475–483 (2017).
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. and Sudoplatov S. V., “Vaught’s conjecture for quite \( o \)-minimal theories,” Ann. Pure Appl. Logic, vol. 168, no. 1, 129–149 (2017).
Kulpeshov B. Sh., “Countably categorical quite \( o \)-minimal theories,” J. Math. Sci., vol. 188, no. 4, 387–397 (2013).
Kulpeshov B. Sh., “Criterion for binarity of \( \aleph_{0} \)-categorical weakly \( o \)-minimal theories,” Ann. Pure Appl. Logic, vol. 45, no. 3, 354–367 (2007).
Funding
This research has been funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP08855544).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kulpeshov, B.S., Mustafin, T.S. Almost \( \omega \)-Categorical Weakly \( o \)-Minimal Theories of Convexity Rank 1. Sib Math J 62, 52–65 (2021). https://doi.org/10.1134/S0037446621010067
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446621010067