- the
standard ZFC
axiomatization of set theory. Czesław Ryll-Nardzewski
proved that
Peano arithmetic cannot be
finitely axiomatized, and
Richard Montague...
-
there are
certain consistent bodies of
propositions with no
recursive axiomatization. Typically, the
computer can
recognize the
axioms and
logical rules...
- 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...
-
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...
-
alternative set theory. In particular, Vopěnka's
Alternative Set
Theory (1979)
axiomatizes the
concept of semiset,
supplemented with
several additional principles...
-
Sanders Peirce provided an
axiomatization of natural-number arithmetic. In 1888,
Richard Dedekind proposed another axiomatization of natural-number arithmetic...
- 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...
-
constructions in
their own right. In particular, the
definition of a
quandle axiomatizes the
properties of
conjugation in a group. In 1943,
Mituhisa Takasaki...
-
Schreier gave the
definition in
terms of
positive cone in 1926,
which axiomatizes the
subcollection of
nonnegative elements.
Although the
latter is higher-order...
- (compact
totally disconnected Hausdorff)
topological space. The
first axiomatization of
Boolean lattices/algebras in
general was
given by the
English philosopher...
