- In
mathematics and logic, an
axiomatic system is a set of
formal statements (i.e. axioms) used to
logically derive other statements such as
lemmas or theorems...
-
There have been
several attempts in
history to
reach a
unified theory of mathematics. Some of the most
respected mathematicians in the
academia have expressed...
-
logician Charles Sanders Peirce. It was
taken as an
axiom in his
first axiomatisation of
propositional logic. It can be
thought of as the law of excluded...
- what we call the
substitutional axiomatisation. Both
formalisations have variables, but
where the one-rule
axiomatisation has
schematic variables that are...
-
meaning of the higher-order
domains is
partly determined by an
explicit axiomatisation,
drawing on type theory, of the
properties of the sets or functions...
- him his
theory of probability." Yet
Andrey Kolmogorov,
whose rival axiomatisation was
better received, was less severe: "The
basis for the applicability...
-
weakening the
above requirement of ω-consistency to
simple consistency;
Axiomatisation of the core of Gödel's
result in
terms of a
modal language, provability...
- of the
axioms of
plane geometry—though
Proclus tells of an
earlier axiomatisation by
Hippocrates of Chios. In the 17th century,
Descartes introduced Cartesian...
-
Applications of
measures include the
Lebesgue integral, Kolmogorov's
axiomatisation of
probability theory, and
ergodic theory.[citation needed] Knot theory...
-
formalized at this time.
Giuseppe Peano provided in 1888 a
complete axiomatisation based on the
ordinal property of the
natural numbers. The last Peano's...
