-
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...
- 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...
- 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...
-
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...
- is a
complemented distributive lattice. The
section on
axiomatization lists other axiomatizations, any of
which can be made the
basis of an
equivalent definition...
- In mathematics,
Robinson arithmetic is a
finitely axiomatized fragment of first-order
Peano arithmetic (PA),
first set out by
Raphael M.
Robinson in 1950...
- (compact
totally disconnected Hausdorff)
topological space. The
first axiomatization of
Boolean lattices/algebras in
general was
given by the
English philosopher...
-
previous work by Pasch. The
success in
axiomatizing geometry motivated Hilbert to s****
complete axiomatizations of
other areas of mathematics, such as...
