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

plural of axiom system

(set theory) One of the axioms of set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty; any version of said axiom, for example specifying the cardinality of the number of sets from which choices are made.

(set theory) A weaker form of the axiom of choice that states that every countable collection of nonempty sets must have a choice function; equivalently, the statement that the direct product of a countable collection of nonempty sets is nonempty.

(set theory) The axiom that the power set of any set exists and is a valid set, which appears in the standard axiomatisation of set theory, ZFC.

Synonym of non-aggression principle