RUDN Journal of PhilosophyRUDN Journal of Philosophy2313-23022408-8900Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)11724An Ontology of Quantum MathematicsVasyukovV LКафедра истории и философии науки; Институт философии РАН; Institute of Philosophy Russian Academy of Sciences-Institute of Philosophy Russian Academy of Sciences150320093577012092016Copyright © 2009, Vasyukov V.L.2009A claim that mathematics would be formalized within the framework of a non-classical logic would be accepted in a twofold manner. It caused by the reason that non-classical mathematics ontology (universe) might be either global or local regarding not only classical but all other non-classical mathematics ontology. The construction of quantos (quantum topos) as categorical global universe allows to extend this claim for the case of quantum mathematics.ontologyquantum mathematicsnon-classical logicset theoryquantosонтологияквантовая математиканеклассическая логикатеория множествквантосы