Abstract

The starting point of this work is the existence of historical paradoxes in the set theory. These are: Russell's paradox, applied to the set W, Cantor's, for the set U, and Burali-Forti's, of the set Omega. A systematic analysis aimed at the simplification and the refining of such paradoxes showed that: there exist at least eight contradictory expressions instead of three; another contradictory set is suggested by an extension of Burali-Forti's paradox; almost all of the contradictions apply to more than one paradoxical set