Zermelo set theory

English

Alternative forms

• Zermelo's set theory

Etymology

After German mathematician Ernst Zermelo, who introduced the theory in a paper in 1908.

Noun

Zermelo set theory

1. (set theory) An early and influential axiomatisation of set theory.
   • 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.

   • 2001, José Ferreirós, Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics‎^[1], Springer (Birkhäuser), page 338:

     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].

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

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

Translations

early axiomatisation of set theory

• Italian: teoria degli insiemi di Zermelo f

See also

• ZF
• ZFC

Further reading

• Zermelo–Fraenkel set theory on Wikipedia.Wikipedia
• S (set theory) on Wikipedia.Wikipedia
• Z notation on Wikipedia.Wikipedia
• Zermelo Set Theory on Wolfram MathWorld