Named set theory

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Named set theory is a branch of theoretical mathematics that studies the structures of names. The named set is a theoretical concept that generalizes the structure of a name described by Frege. Its generalization bridges the descriptivists theory of a name, and its triad structure (name, sensation and reference),^[1] with mathematical structures that define mathematical names using triplets. It deploys the former to view the latter at a higher abstract level that unifies a name and its relationship to a mathematical structure as a constructed reference. This enables all names in science and technology to be treated as named sets or as systems of named sets.

Informally, named set theory is a generalization that studies collections of objects (may be, one object) connected to other objects (may be, to one object). The paradigmatic example of a named set is a collection of objects connected to its name. Mathematical examples of named sets are coordinate spaces (objects are points and coordinates are names of these points), vector fields on manifolds (objects are points of the manifold and vectors assigned to points are names of these points), binary relations between two sets (objects are elements of the first set and elements of the second set are names) and fiber bundles (objects form a topological space, names from another topological space and the connection is a continuous projection). The language of named set theory can be used in the definitions of all of these abstract objects.