СВОЙСТВА ПОНЯТИЙ СВОБОДЫ И НЕЗАВИСИМОСТИ ДЛЯ ГИПЕРГРАФОВ МОДЕЛЕЙ ВПОЛНЕ О-МИНИМАЛЬНЫХ ТЕОРИЙ С НЕМАКСИМАЛЬНЫМ ЧИСЛОМ СЧЕТНЫХ МОДЕЛЕЙ
Kulpeshov B.S. Sudoplatov S.V.
2024Sobolev Institute of Mathematics
Siberian Electronic Mathematical Reports
2024#21Issue 1164 - 177 pp.
We study properties of the concepts of freedom and independence for hypergraphs of models of a quite o-minimal theory with few countable models. Conditions for freedom of sets of realizations of isolated and non-isolatcd types arc characterized in terms of the convexity rank. In terms of weak orthogonality, characterizations of the relative independence of sets of realizations of isolated and non-isolatcd types of convexity rank 1 arc obtained. Conditions for freedom and independence of equivalence classes are established, indicating the finite rank of convexity of a non-algebraic isolated type of a given theory. In terms of equivalence classes, the conditions for the relative freedom of isolated and nonisolated types are characterized. In terms of weak orthogonality, characterizations of the relative independence of sets of realizations of isolated and non-isolatcd types over given equivalence relations are obtained. The transfer of the property of relative freedom of types under the action of definable bijections is proved. It is shown that for the specified conditions the non-maximality of the number of countable models of the theory is essential.
free set , hypergraph of models , independent-sets , quite o-minimality
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Institute of Mathematics and Mathematical Modeling, Shevchenko street 28, Almaty, 050010, Kazakhstan
Kazakh British Technical University, ToLE BI STREET59, Almaty, 050000, Kazakhstan
Novosibirsk State Technical University, K. Marx avenue, 20, Novosibirsk, 630073, Russian Federation
Sobolev Institute of Mathematics, Academician Koptyug avenue, 4, Novosibirsk, 630090, Russian Federation
Institute of Mathematics and Mathematical Modeling
Kazakh British Technical University
Novosibirsk State Technical University
Sobolev Institute of Mathematics
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