Pure second-order logic.
Nicholas Denyer · Notre Dame Journal of Formal Logic · 1992
Pure second-order predicate calculus is a predicate calculus where the only variables are predicate variables.In it, logical truth is decidable, and semantic consequence is compact.Pure second-order functional calculus is a functional calculus where the only variables are function variables.In it, semantic consequence is not compact, and there is no complete proof procedure for logical truth.The language of the pure second-order predicate calculus consists of those formulas of the second-order predicate calculus whose only variables are predicate variables.A statement of its semantics will help to elucidate my notational conventions.A model 9JJ is a pair , where 2) is a domain of individuals, and 9ί is a function such that:1. an atomic formula ff lf ...