-
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...
- the
standard ZFC
axiomatization of set theory. Czesław Ryll-Nardzewski
proved that
Peano arithmetic cannot be
finitely axiomatized, and
Richard Montague...
-
arithmetic of the
natural numbers and
which are
consistent and
effectively axiomatized.
Particularly in the
context of first-order logic,
formal systems are...
-
possessed by all
natural numbers ("Induction axiom"). In mathematics,
axiomatization is the
process of
taking a body of
knowledge and
working backwards towards...
- (compact
totally disconnected Hausdorff)
topological space. The
first axiomatization of
Boolean lattices/algebras in
general was
given by the
English philosopher...
-
constructions in
their own right. In particular, the
definition of a
quandle axiomatizes the
properties of
conjugation in a group. In 1942,
Mituhisa Takasaki [ja]...
-
alternative set theory. In particular, Vopěnka's
Alternative Set
Theory (1979)
axiomatizes the
concept of semiset,
supplemented with
several additional principles...
- 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...
- a
modern treatment of
Euclidean geometry.
Other well-known
modern axiomatizations of
Euclidean geometry are
those of
Alfred Tarski and of
George Birkhoff...
- b)\mid c)\mid (a\mid ((a\mid c)\mid a))=c} is
sufficient to
completely axiomatize Boolean algebra. It is also
possible to find
longer single axioms using...
