Axiomatisability

Axiomatisability refers to whether a particular set of structures or systems can be fully described using a finite or recursive set of rules or statements, called axioms. In logical and mathematical contexts, it means that the properties and behaviors of these systems can be captured completely by a well-defined collection of foundational principles. If a class of structures is axiomatisable, then its entire behavior and relationships can be derived from these rules, making it possible to understand, analyze, and work with the system in a systematic and precise way.