- first-order
language (in fact, most sets have this property). First-order
axiomatizations of
Peano arithmetic have
another technical limitation. In second-order...
- 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...
- 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...
- 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...
-
there are
certain consistent bodies of
propositions with no
recursive axiomatization. Typically, the
computer can
recognize the
axioms and
logical rules...
- the
standard ZFC
axiomatization of set theory. Czesław Ryll-Nardzewski
proved that
Peano arithmetic cannot be
finitely axiomatized, and
Richard Montague...
- 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...
- In mathematics,
Robinson arithmetic is a
finitely axiomatized fragment of first-order
Peano arithmetic (PA),
first set out by
Raphael M.
Robinson in 1950...
- the same set, in
either the
strict weak
ordering or
total preorder axiomatizations. However, a
different kind of move is possible, in
which the weak orderings...
- that, for
Peano arithmetic and any
stronger theories with
effective axiomatizations,
tolerance is
equivalent to Π 1 {\displaystyle \Pi _{1}} -consistency...
