- such as groups). Thus non-logical
axioms,
unlike logical axioms, are not tautologies.
Another name for a non-logical
axiom is postulate.
Almost every modern...
-
mathematical logic, the
Peano axioms (/piˈɑːnoʊ/, [peˈaːno]), also
known as the Dedekind–Peano
axioms or the
Peano postulates, are
axioms for the
natural numbers...
- the
axiom of
choice for
their proofs.
Contemporary set
theorists also
study axioms that are not
compatible with the
axiom of choice, such as the
axiom of...
- the
axioms of Zermelo–Fraenkel set theory. Most of the
axioms state the
existence of
particular sets
defined from
other sets. For example, the
axiom of...
- not as an
axiom but as a
definition of equality. Then it is
necessary to
include the
usual axioms of
equality from
predicate logic as
axioms about this...
-
branches of
mathematics and
philosophy that use it, the
axiom of
infinity is one of the
axioms of Zermelo–Fraenkel set theory. It
guarantees the existence...
-
probability axioms are the
foundations of
probability theory introduced by
Russian mathematician Andrey Kolmogorov in 1933.
These axioms remain central...
-
axioms can be
formulated which are
logically equivalent to the
parallel postulate (in the
context of the
other axioms). For example, Playfair's
axiom...
- sets of
axioms, Pasch's
axiom can be
proved as a theorem; it is a
consequence of the
plane separation axiom when that is
taken as one of the
axioms. Hilbert...
-
axiom Axiom of
constructibility Rank-into-rank Kripke–Platek
axioms Diamond principle Parallel postulate Birkhoff's
axioms (4
axioms) Hilbert's
axioms (20...
