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An Approach to Fundamental Concepts of Mathematics I: Set, Structure, System, Model
Boris Chendov
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DOI:doi: 10.17265/2159-5291/2018.07.003
Institute of philosophy at Bulgarian Academy of sciences, Section of Logic, Sofia, Bulgaria
In the introduction a preliminary consideration of the sense of concepts “set”, “structure”, “system”, and “model”, as well as of the connection between them is proposed and on the basis of its results the task of investigation of abstract bases of system (in particular reconsideration of concept “abstract set”), of abstract structure, abstract system and of S-Model is formulated. The first section is devoted to formulation of an approach to construction of aggregate theory regarded as an analog of moderate constructive set theory: the relations “inclusion” and “equivalence” between aggregates and the operations on aggregates “union”, “intersection, “difference” and “compliment” are introduced. Definition of the concept “a-system” as well as of its a-structure on the space of aggregates is defined. A special attention is shown to similarity and essential difference between aggregate theory and set theory as well as to the fact that the famous paradoxes of Cantor and Russell in the Cantor’s set theory take no place in the aggregate theory. Further a variant of Cantor’s set theory called restricted discrete set theory is considered. The second section is devoted to formulation of an approach to construction of algebra of a-systems. At the end the concept of system of successive systems (SSS), is introduced.
Aggregate, set, structure, system, model.
Chendov B. 2018. "An Approach to Fundamental Concepts of Mathematics I: Set, Structure, System, Model" Journal of Mathematics and System Science 8 (2018) 187-200.
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