Логические и эпистемологические аспекты конструктивного знания

5 октября Владимир Леонидович Васюков выступил с докладом ''Internal Logic of the H-B topos and Universal Metalogic'' на воркшопе "Логические и эпистемологические аспекты конструктивного знания"

Abstract: Chris Mortensen in his book ”Inconsistent Mathematics” introduced the notion of complement topos such that its internal logic is dual to the usual logic of standard topos. Since the complement classifier is indistinguishable (via categorial methods) from the standard subobject classifier, any topos can be described as H-B topos, in which we have both Heyting and co-Heyting (Brouwerian) algebras of subobjects. We propose a formulation of internal logic of such H-B topos based on C.Rauszer’s H-B logic. Taking into account the fact that the category Log of logical systems contains both types of subobject classifiers we adopt this approach for the case of Log.