Type theory | Lambda calculus | Proof theory

System U

In mathematical logic, System U and System U− are pure type systems, i.e. special forms of a typed lambda calculus with an arbitrary number of sorts, axioms and rules (or dependencies between the sorts). They were both proved inconsistent by Jean-Yves Girard in 1972. This result led to the realization that Martin-Löf's original 1971 type theory was inconsistent as it allowed the same "Type in Type" behaviour that Girard's paradox exploits. (Wikipedia).

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Related pages

Type inhabitation | First-class function | Parametric polymorphism | Pure type system | Curry–Howard correspondence | Intuitionistic type theory | Mathematical logic | Structure (mathematical logic) | System F | Type constructor | Type theory | Russell's paradox | Typed lambda calculus | Many-sorted logic | Kind (type theory) | Naive set theory