A New Version of Orthogonality for 1-Types in Weakly o-Minimal Theories
Kulpeshov B.S. Sudoplatov S.V.
September 2024Springer
Algebra and Logic
2024#63Issue 4270 - 283 pp.
We introduce a new version of orthogonality for nonalgebraic 1-types in weakly o-minimal theories, that of almost quite orthogonality. It is stated that the non almost quite orthogonality relation is an equivalence relation. The main result is a criterion for a weakly o-minimal theory of finite convexity rank with 1 < I(T, ω) < 2ω to have exactly 3m6l countable pairwise nonisomorphic models for some nonnegative integers m, l < ω in terms of the orthogonality version presented.
convexity rank , countable model , orthogonality , Vaught’s conjecture , weak o-minimality
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Kazakh-British Technical University. Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science RK, Alma-Ata, Kazakhstan
Sobolev Institute of Mathematics, Novosibirsk, Russian Federation
Kazakh-British Technical University. Institute of Mathematics and Mathematical Modeling
Sobolev Institute of Mathematics
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