### Some articles on *impredicative*:

Axiom Of Reducibility - Criticism of The Axiom of Reducibility - Stephen Kleene 1952

... from the discovery of the paradoxes, Russell excluded

... 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 - Π1

... arithmetical transfinite recursion and is fully

_{1}Comprehension Π1_{1}-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

... 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 -

... an example of the paradoxes that result from an

**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 ...Main Site Subjects

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