FOUNDATIONS OF MATHEMATICS: SET THEORY VS. TYPE THEORY
Lev Dmitrievich Lamberov
Ural Federal University, 620000, 51, av. Lenin, Ekaterinburg, Russia
Keywords: теория множеств, теория типов, гомотопии, основания математики, set theory, type theory, homotopies, foundations of mathematics
Abstract
The paper deals with a brief history of the development of set theory as the foundations of mathematics, and a brief history of the formation process of the type theory. The paper contains a detailed comparison of set theory and type theory, discussion of the problems of the set theory, and the advantages of the type theory as the foundations of mathematics. In addition, the article discusses the pragmatic aspect of the type theory as the foundations of mathematics and contains a brief overview of a modern version of the type theory, namely homotopy type theory.
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