- In
mathematics and logic, an
axiomatic system is any set of
primitive notions and
axioms to
logically derive theorems. A
theory is a consistent, relat...
- by
Skolem (1922: p. 295). Skolem's
paradox is that
every countable axiomatisation of set
theory in first-order logic, if it is consistent, has a model...
- y {\displaystyle \forall xPxy\to Pty} .
There are
several variant axiomatisations of
predicate logic,
since for any
logic there is
freedom in choosing...
- mathematics, and it or an
equivalent appears in just
about any
alternative axiomatisation of set theory. However, it may
require modifications for some purposes...
-
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...
-
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...
- of the
axioms of
plane geometry—though
Proclus tells of an
earlier axiomatisation by
Hippocrates of Chios. In the 17th century,
Descartes introduced Cartesian...
-
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...
- him his
theory of probability." Yet
Andrey Kolmogorov,
whose rival axiomatisation was
better received, was less severe: "The
basis for the applicability...
- in each
uncountable cardinal. Schanuel's
conjecture is part of this
axiomatisation, and so the
natural conjecture that the
unique model of cardinality...
