- in
other words, sets shouldn't
refer to themselves). In some
other axiomatizations of ZF, this
axiom is
redundant in that it
follows from the
axiom schema...
- the
standard ZFC
axiomatization of set theory. Czesław Ryll-Nardzewski
proved that
Peano arithmetic cannot be
finitely axiomatized, and
Richard Montague...
- method".
Church was
evidently unaware that
string theory already had two
axiomatizations from the 1930s: one by Hans
Hermes and one by
Alfred Tarski. Coincidentally...
- first-order
language (in fact, most sets have this property). First-order
axiomatizations of
Peano arithmetic have
another technical limitation. In second-order...
- a
modern treatment of
Euclidean geometry.
Other well-known
modern axiomatizations of
Euclidean geometry are
those of
Alfred Tarski and of
George Birkhoff...
- In
topology and
related branches of mathematics, the
Kuratowski closure axioms are a set of
axioms that can be used to
define a
topological structure on...
-
previous work by Pasch. The
success in
axiomatizing geometry motivated Hilbert to s****
complete axiomatizations of
other areas of mathematics, such as...
-
theories of
Peano arithmetic and any
stronger theories with
effective axiomatizations,
cointerpretability is
equivalent to Σ 1 {\displaystyle \Sigma _{1}}...
-
possessed by all
natural numbers ("Induction axiom"). In mathematics,
axiomatization is the
process of
taking a body of
knowledge and
working backwards towards...
-
Stanford University,
retrieved 19
October 2019 Mendelson, "6.
Other Axiomatizations" of Ch. 1 Mendelson, "3. First-Order Theories" of Ch. 2 Mendelson,...
