Abstract: 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-isolated types are 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-isolated types of convexity rank 1 are obtained. Conditions for freedom and independence of equivalence classes are established, indicating the nite rank of convexity of a nonalgebraic 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-isolated types over given equivalence relations are obtained. The transfer of the property of relative freedom of types under the action of de nable bijections is proved. It is shown that for the specifed conditions the non-maximality of the number of countable models of the theory is essential.

Cite: Кулпешов Б.Ш. , Судоплатов С.В.
Свойства понятий свободы и независимости в гиперграфах моделей вполне о-минимальных теорий с немаксимальным числом счетных моделей
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2024. Т.21. №1. С.164-177. DOI: 10.33048/semi.2024.21.011 WOS Scopus РИНЦ

Dates:

Submitted:	Oct 15, 2023
Accepted:	Dec 15, 2023
Published print:	Feb 28, 2024
Published online:	Feb 28, 2024

Identifiers:

Web of science:	WOS:001200266800002
Scopus:	2-s2.0-85191871140
Elibrary:	82336236

Citing: Пока нет цитирований

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