НЕЗАВИСИМОСТЬ АКСИОМАТИЧЕСКОЙ СИСТЕМЫ

Axiomatic System, Independence of

A characteristic of axiomatics (see Axiomatic Method). If not a single axiom underlying a deductive system can be inferred by the rules of deduction of this system, such a system of axioms is called independent. Otherwise, the system of axioms is dependent. A study of any axiomatic system from this point of view is important not only for simplifying axiomatics. It may be important in principle. Thus, establishment of the independence of Euclid's fifth postulate in the system of axioms of geometry facilitated the development of non-Euclidean geometries.