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 Kulpeshov, B.Sh., Sudoplatov, S.V., Properties of concepts of freedom and independence for hypergraphs of models of quite o-minimal theories with few countable models.© 2024 Êóëïåøîâ Á.Ø., Ñóäîïëàòîâ Ñ.Â.. Ðàáîòà âûïîëíåíà ïðè ôèíàíñîâîé ïîääåðæêå Êîìèòåòà íàóêè Ìèíèñòåðñòâà íàóêè è âûñøåãî îáðàçîâàíèÿ Ðåñïóáëèêè Êàçàõñòàí (ãðàíòû BR20281002 è ÀÐ19674850), à òàêæå â ðàìêàõ ãîñóäàðñòâåííîãî çàäàíèÿ Èíñòèòóòà ìàòåìàòèêè èì.Ñ.Ë.