 When second-order logic is used as a foundation for mathematics, a situation may emerge in which third order logic is needed. For example, a topology is usually defined as a family of sets and is therefore a third order object. It would be well in the spirit of second-order logic to simply include third (or higher) order logic when needed. Naturally, the Comprehension Axiom Schema and the Axioms of Choice have to be then assumed for third order quantifiers.