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

(mathematics) Any of a set of fundamental axioms describing the natural numbers and their relationships.

plural of axiom schema

plural of axiom scheme

(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.

(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.

(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).

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