(logic) A formula in the language of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.

(logic) A formula in the language of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.

A set of axioms or axiom schemata from which theorems can be derived.

(mathematics) The following axiom (applied to an ordered field): for any subset of the given ordered field, if there is any upper bound for this subset, then there is also a supremum for this subset, and this supremum is an element of the given ordered field (though not necessarily of the subset).

(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