-
impossible to
axiomatize ZFC
using only
finitely many axioms. On the
other hand, von Neumann–Bernays–Gödel set
theory (NBG) can be
finitely axiomatized. The ontology...
-
whereas other set theories, such as von Neumann–Bernays–Gödel set theory,
axiomatize the
notion of "proper class", e.g., as
entities that are not
members of...
- the
standard ZFC
axiomatization of set theory. Czesław Ryll-Nardzewski
proved that
Peano arithmetic cannot be
finitely axiomatized, and
Richard Montague...
- self-evident in
nature (e.g., the
parallel postulate in
Euclidean geometry). To
axiomatize a
system of
knowledge is to show that its
claims can be
derived from a...
-
possessed by all
natural numbers ("Induction axiom"). In mathematics,
axiomatization is the
process of
taking a body of
knowledge and
working backwards towards...
-
Sanders Peirce provided an
axiomatization of natural-number arithmetic. In 1888,
Richard Dedekind proposed another axiomatization of natural-number arithmetic...
- a
modern treatment of
Euclidean geometry.
Other well-known
modern axiomatizations of
Euclidean geometry are
those of
Alfred Tarski and of
George Birkhoff...
- (compact
totally disconnected Hausdorff)
topological space. The
first axiomatization of
Boolean lattices/algebras in
general was
given by the
English philosopher...
- In 1936,
Alfred Tarski gave an
axiomatization of the real
numbers and
their arithmetic,
consisting of only the
eight axioms shown below and a mere four...
- Hilbert's
sixth problem is to
axiomatize those branches of
physics in
which mathematics is prevalent. It
occurs on the
widely cited list of Hilbert's problems...
