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The solution proposed by Chwistek was prompted by a constructivistic/predicativistic conception.
With this, too, constructivistic criticism of set theory began to emerge, as Leopold Kronecker started to make objections to such infinitary procedures.
I believe that the basic problems of set theory, such as Cantor's continuum problem, will be solved satisfactorily only with the help of stronger axioms of this kind, which in a sense are opposite or complimentary to the constructivistic interpretation of mathematics.