(set theory) One of the axioms in axiomatic set theory, equivalent to the statement that two sets are equal if and only if they contain the same elements.

(set theory) One of the axioms in axiomatic set theory, equivalent to the statement that every non-empty set contains a member that is disjoint from that set.

(set theory) One of the axioms in axiomatic set theory, equivalent to the statement that a union exists for any set, containing exactly all the elements contained within the sets within that set.

(set theory) One of the axioms in axiomatic set theory, equivalent to the statement that if two sets exist, there exists a set with those two sets as its sole elements.

(set theory) One of the axioms in axiomatic set theory that guarantees the existence of an infinite set.

plural of axiom schema

(mathematics) Any of the several axioms that an object should meet to be considered a mathematical field.

(geometry) A statement in plane geometry, used implicitly by Euclid, which cannot be derived from Euclid's postulates. It states that, if a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side.

Alternative form of non-aggression axiom

(physics) Any of a number of axioms representing an attempt at a mathematically rigorous formulation of quantum field theory.