# Impredicative

### Some articles on impredicative:

Axiom Of Reducibility - Criticism of The Axiom of Reducibility - Stephen Kleene 1952
... from the discovery of the paradoxes, Russell excluded impredicative definitions by his ramified theory of types (1908, 1910)" ... Kleene observes that "to exclude impredicative definitions within a type, the types above type 0 are further separated into orders ... to construct the familiar analysis, which contains impredicative definitions ...
Reverse Mathematics - The Big Five Subsystems of Second Order Arithmetic - Π11 Comprehension Π11-CA
... arithmetical transfinite recursion and is fully impredicative ... equivalent to several statements of descriptive set theory whose proofs make use of strongly impredicative arguments this equivalence shows that these impredicative ...
Type Theory - History - 1900–1927 - The 1908 "ramified" Theory of Types
... Then to exclude impredicative definitions within a type, the types above type 0 are further separated into orders ... to construct the familiar analysis, which we saw above contains impredicative definitions ... properties are considered to exist, then the axiom means that to every impredicative definition within a given type there is an equivalent predicative one (Kleene 195244-45 ...
Parametric Polymorphism - Predicativity and Impredicativity - Impredicative Polymorphism
... Impredicative polymorphism (also called first-class polymorphism) is the most powerful form of parametric polymorphism ... A definition is said to be impredicative if it is self-referential in type theory this allows the instantiation of a variable in a type with any type, including polymorphic types, such as itself ... In type theory, the most frequently studied impredicative typed λ-calculi are based on those of the lambda cube, especially System F ...
Propositional Formula - Impredicative Propositions
... an example of the paradoxes that result from an impredicative definition -- that is, when an object m has a property P, but the object m is defined in terms of property P ... The best advice for a rhetorician or one involved in deductive analysis is avoid impredicative definitions but at the same time be on the lookout for them ...