- theory, but the
latter can be
finitely axiomatized. The set
theory New
Foundations can be
finitely axiomatized through the
notion of stratification. Schematic...
-
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...
-
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...
- logic: Double-negation
elimination (DNE) is the
strongest principle,
axiomatized ¬ ¬ A ⟹ A {\displaystyle \neg \neg A\implies A} , and when it is added...
- axioms, and it was
thought that, in principle,
every theory could be
axiomatized in this way and
formalized down to the bare
language of
logical formulas...
- In mathematics,
Robinson arithmetic is a
finitely axiomatized fragment of first-order
Peano arithmetic (PA),
first set out by
Raphael M.
Robinson in 1950...
-
subtraction and
division instead of
addition and multiplication,
which are
axiomatized in such a way to
avoid proving sentences that
correspond to the totality...
- Springer-Verlag, ISBN 0-387-90092-6 - "Naive"
means that it is not
fully axiomatized, not that it is
silly or easy (Halmos's
treatment is neither). Jech,...
- 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...
