English Wikipedia - The Free Encycl...
Download this dictionary
Von Neumann–Bernays–Gödel set theory
In the
foundations of mathematics
,
von Neumann–Bernays–Gödel set theory
(
NBG
) is an
axiomatic set theory
that is a
conservative extension
of the canonical
Zermelo–Fraenkel set theory
(ZFC). A statement in the language of ZFC is provable in NBG
if and only if
it is provable in ZFC. The
ontology
of NBG includes
proper classes
, objects having members but that cannot be members of other entities. NBG's principle of
class comprehension
is
predicative
;
quantified
variables in the defining
formula
can range only over sets. Allowing
impredicative
comprehension turns NBG into
Morse-Kelley set theory
(MK). NBG, unlike ZFC and MK, can be
finite
ly axiomatized.
See more at Wikipedia.org...
© This article uses material from
Wikipedia
®
and is licensed under the
GNU Free Documentation License
and under the
Creative Commons Attribution-ShareAlike License