Named Set Theory Axiomatization : T Theory

Named sets is a basic mathematical structure, providing a unified foundations for mathematics and encompassing different generalizations of sets that are studied in mathematics and used in applications. The most important and popular of these generalizations are multisets and fuzzy sets. An axiomatization of the theory of named sets based is given and some properties of named sets are derived from these axioms. This axiom system has been developed with a threefold aim. The first goal is to show that on a formal level the concept of a named set is independent of the concept of a set. The second target is to be able to develop a sufficiently powerful set theory (in this case, it is ) and to have a model of in such an established theory as . The third intention is to be able to develop category theory independently of set theory