- 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...
- the
standard ZFC
axiomatization of set theory. Czesław Ryll-Nardzewski
proved that
Peano arithmetic cannot be
finitely axiomatized, and
Richard Montague...
-
Sanders Peirce provided an
axiomatization of natural-number arithmetic. In 1888,
Richard Dedekind proposed another axiomatization of natural-number arithmetic...
-
possessed by all
natural numbers ("Induction axiom"). In mathematics,
axiomatization is the
process of
taking a body of
knowledge and
working backwards towards...
- 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...
-
alternative set theory. In particular, Vopěnka's
Alternative Set
Theory (1979)
axiomatizes the
concept of semiset,
supplemented with
several additional principles...
- In mathematics,
Robinson arithmetic is a
finitely axiomatized fragment of first-order
Peano arithmetic (PA),
first set out by
Raphael M.
Robinson in 1950...
-
arithmetic of the
natural numbers and
which are
consistent and
effectively axiomatized.
Particularly in the
context of first-order logic,
formal systems are...
-
negation (¬),
implication (→) and
propositional symbols. A well-known
axiomatization,
comprising three axiom schemata and one
inference rule (modus ponens)...