axiomet

Axiomet is a term encountered in some discussions of logic and the foundations of mathematics to denote a meta-system that governs the selection, formation, and use of axioms within a theory. It can be thought of as a framework at the metalevel that abstracts the criteria by which axioms are judged, added, or discarded.

Because "axiomet" is not standard, there is no single formal definition. In different sources it can refer to (1) a proposed set of meta-axioms that constrain an axiomatic system, (2) a general study of the rules and properties of axiom systems (metaxiomology), or (3) a philosophical notion capturing how metatheoretical commitments shape the axioms used in a theory.

Relation to other concepts: An axiomet is distinct from an axiom (a statement accepted within a theory) and from metatheory (the study of a theory). It is positioned at the interface, aiming to formalize the criteria by which the axioms themselves are justified, validated, or invalidated. In practice, discussions of axiomet often appear in explorations of consistency, completeness, and the limits of axiomatisation.

Status and reception: The term has limited adoption and is not part of standard curricula or widely cited literature. Its meaning depends on the author, which can lead to definitional drift. When used, it is typically clarified in context, with explicit meta-axioms or meta-logical principles described alongside it.