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Название: Constructible sets with applications
Автор: Mostowski A.
The present book was originally planned as a companion volume to the above mentioned work. In the course of the writing it I realized, however, that it would not be convenient to base the exposition on the Zermelo-Fraenkel type of axioms adopted in the earlier book. It proved especially difficult to arrange the exposition of metaathematical results without using the notion of classes, which we had avoided in the book on the "classical" parts of set theory. I changed therefore to a stronger system, in which classes were allowed, and decided to present results concerning the Zermelo-Fraenkel set theory on the basis of Morse's theory of classes. It is debatable whether it would not have been wiser to present the meta-mathematical results concerning the Gddel-Bernays set theory on the basis of the same theory or perhaps even on the basis of a finitary meta-mathematics. I believe that there are advantages and disadvantages in each of these approaches. The advantage of basing the exposition on Morse's axioms is that the consistency of the Zermelo-Fraenkel set theory and the existence of its well-founded models are provable and need not be assumed as hypotheses.