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Abstract
After a brief historical overview, 20th-Century Mathematics is characterized by the priority of structures over mathematical objects. The usual ways of conceptualizing "structure", "system", and "set" are discussed, in order to show the way inconsistencies appear in the use of "structure", and to show the advantages of using a version of general systems theory adapted to modern mathematics. The concept of mathematical system is worked out, deploying its material, active, and theoretical aspects, to which there co- rrespond the substratum (set of objects), the dynamics (set of transformations), and the statics (set of relations), i. e., the structure of the mathematical system. The paper deve- lops the different types of mathematical systems currently in use, from natural number systems to categories, to show the appropriateness of the theory developed in it, and its descriptive power.
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