Definition of: metamathematics

(met′ə·math′ə·mat′iks) noun
That branch of mathematics which is concerned with the formalized and rigorously logical treatment of pure symbols, having regard only to internal consistency and the establishment of absolute proofs of the validity of a given set of axioms, postulates, theorems, etc., within a mathematical system.
—met′a·math′e·mat′i·cal adjective