-
function type is
consistent with the
types of the arguments. In an
impredicative system, T {\displaystyle T} may be any type whatsoever,
including a...
- mathematics,
something that is
impredicative is a self-referencing definition.
Roughly speaking, a
definition is
impredicative if it
invokes (mentions or...
-
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...
- this
makes its
definition impredicative.
Kleene ****erts that
attempts to
argue this away can be used to
uphold the
impredicative definitions in the paradoxes...
-
proposed both
intensional and
extensional variants of the
theory and
early impredicative versions,
shown to be
inconsistent by Girard's paradox, gave way to...
- theory,
Springer 1989 ISBN 0-387-51842-8 (for
Veblen hierarchy and some
impredicative ordinals). This is
probably the most
readable book on
large countable...
-
theory whose proofs make use of
strongly impredicative arguments; this
equivalence shows that
these impredicative arguments cannot be removed. The following...
- first-class data type
Generic Haskell, C++11 first-class
polymorphism impredicative polymorphism first-class
message dynamic messages (method calls) Smalltalk...
- thus
giving the
first example of a
predicative result with a
provably impredicative proof. This case of the
theorem is
still provable by Π1 1-CA0, but by...
-
rather than the
theory of
simple types. (See "Ramified
Hierarchy and
Impredicative Principles".) An
analysis of the
paradoxes to be
avoided shows that...
