- mathematics,
something that is
impredicative is a self-referencing definition.
Roughly speaking, a
definition is
impredicative if it
invokes (mentions or...
-
function type is
consistent with the
types of the arguments. In an
impredicative system, T {\displaystyle T} may be any type whatsoever,
including a...
- first-class data type
Generic Haskell, C++11 first-class
polymorphism impredicative polymorphism first-class
message dynamic messages (method calls) Smalltalk...
-
impredicative expressions such as x ε x can be
treated in his logic,
Russell proposed, as a kind of
working hypothesis, that all such
impredicative definitions...
-
proposed both
intensional and
extensional variants of the
theory and
early impredicative versions,
shown to be
inconsistent by Girard's paradox, gave way to...
- this
makes its
definition impredicative.
Kleene ****erts that
attempts to
argue this away can be used to
uphold the
impredicative definitions in the paradoxes...
- and set theory. One
major challenge has been the
ordinal analysis of
impredicative theories. The
first breakthrough in this
direction was Takeuti's proof...
- For this reason,
ordinal collapsing functions are
described as an
impredicative manner of
naming ordinals. The
details of the
definition of ordinal...
-
theory whose proofs make use of
strongly impredicative arguments; this
equivalence shows that
these impredicative arguments cannot be removed. The following...
- such that φα(0) = α. This
ordinal is
sometimes said to be the
first impredicative ordinal,
though this is controversial,
partly because there is no generally...
