Naive Set Theory (book)

Naive Set Theory
First edition
AuthorPaul Halmos
Publication date
1960

See also Naive set theory for the mathematical topic.

Naive Set Theory is a mathematics textbook by Paul Halmos providing an undergraduate introduction to set theory.[1] Originally published by Van Nostrand in 1960,[2] it was reprinted in the Springer-Verlag Undergraduate Texts in Mathematics series in 1974.[3]

While the title states that the set theory presented is 'naive', which is usually taken to mean without formal axioms, the book does introduce a system of axioms equivalent to that of ZFC set theory except the Axiom of foundation. It also gives correct and rigorous definitions for many basic concepts.[2][4] Where it differs from a "true" axiomatic set theory book is its character: there are no discussions of axiomatic minutiae, and there is next to nothing about advanced topics such as large cardinals or forcing. Instead, it tries to be intelligible to someone who has never thought about set theory before.

Halmos later stated that it was the fastest book he wrote, taking about six months, and that the book "wrote itself".[5]

  1. ^ Review of Naive Set Theory by H. Mirkil (April 1961), American Mathematical Monthly 68 (4): 392, doi:10.2307/2311615.
  2. ^ a b Review of Naive Set Theory, L. Rieger, MR0114756.
  3. ^ Halmos, Paul (1974). Naive set theory. Undergraduate Texts in Mathematics. Springer-Verlag. doi:10.1007/978-1-4757-1645-0. ISBN 978-0-387-90092-6. MR 0453532.
  4. ^ Review of Naive Set Theory, Alfons Borgers (July 1969), Journal of Symbolic Logic 34 (2): 308, doi:10.2307/2271138.
  5. ^ Ewing, John H.; Gehring, Frederick W., eds. (1991), Paul Halmos: celebrating 50 years of mathematics, Springer-Verlag, Interview of Halmos with Donald J. Albers, p. 16, ISBN 0-387-97509-8.