Georg Сantor as the author of constructions playing fundamental roles in constructive mathematics

An extended version of the author's talk at the meeting of the St. Petersburg Mathematical Society (March 3, 1995), dedicated to the 150th anniversary of G. Cantor's birth, is presented. The following inventions of Cantor and their roles in constructive mathematics are discussed: the system of notation for order-types less than $\varepsilon_0$, a constructive (in essence) definition of the notion of real number, and Cantor's “diagonal” construction. Bibliography: 22 titles.