Zermelo set theory

alternative Zermelo's set theory

1. mathematicsAn early and influential axiomatisation of set theory.

   Z is a formal specification language founded on Zermelo set theory.

   2006, Gerard O'Regan, Mathematical Approaches to Software Quality, Springer, page 20

   2 more examples

   1998, Geoffrey Hellman, 8: Beyond Definitionism—But Not Too Far Beyond, Matthias Schirn (editor), 2003, Paperback, The Philosophy of Mathematics Today, Oxford University Press (Clarendon Press), page 215, The system can be claimed to transcend certain critical limitations of predicative analysis and certain awkwardness of known nominalistic approaches to mathematics at once, and would seem to provide a well-motivated alternative to Zermelo set theory as a framework for scientifically applicable mathematics.

   According to the great logician Alonzo Church, in spite of superficial differences, these two "widely accepted symbolic systems," Zermelo set theory and simple type theory, are "in their currently accepted forms essentially similar" [1939, 69-70].

   2001, José Ferreirós, Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics, Springer (Birkhäuser), page 338