The empty set, the singleton, and the ordered pair

@article{Kanamori2003TheES,
  title={The empty set, the singleton, and the ordered pair},
  author={Akihiro Kanamori},
  journal={Bull. Symb. Log.},
  year={2003},
  volume={9},
  pages={273-298}
}
  • A. Kanamori
  • Published 1 September 2003
  • Philosophy
  • Bull. Symb. Log.
For the modern set theorist the empty set O, the singleton { a }, and the ordered pair 〈 x, y 〉 are at the beginning of the systematic, axiomatic development of set theory, both as a field of mathematics and as a unifying framework for ongoing mathematics. These notions are the simplest building locks in the abstract, generative conception of sets advanced by the initial axiomatization of Ernst Zermelo [1908a] and are quickly assimilated long before the complexities of Power Set, Replacement… 
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