Journal of Mathematical Sciences, Vol. 138, No. 4, 2006 CHARACTERIZATION OF MODEL MIRIMANOVнVON NEUMANN CUMULATIVE SETS E. I. Bunina and V. K. Zakharov UDC 510.223 CONTENTS 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Some Facts From ZermeloнFraenkel Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. Classes in the ZF set theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. Ordinal and cardinals in the

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