set theory

set theory (usually uncountable, plural set theories)

1. (mathematics) The mathematical theory of sets.
   • 1972, Peter W. Zehna, Robert Leo Johnson, Elements of Set Theory, Allyn & Bacon, page 4,

     We mentioned previously that certain paradoxes in set theory arose shortly after Cantor's works were published.

   • 1984, Robert Goldblatt, Topoi, the categorial analysis of logic, p. 9

     The above argument, known as Russell's Paradox, was discovered by Bertrand Russell in 1901. Set theory itself began a few decades earlier with the work of George Cantor.

   • 1994, Yiannis N. Moschovakis, Notes on Set Theory, Springer, page 239,

     The serious study of models of axiomatic set theories depends heavily on methods from mathematical logic which are outside the scope of these Notes.

   • 2012, M. Randall Holmes, Thomas Forster, Thierry Libert, Alternative Set Theories, Dov M. Gabbay, Akihiro Kanimori, John Woods (editors), Sets and Extensions in the Twentieth Century, Elsevier (North-Holland), page 559,

     The one thing that all alternative set theories have in common is the fact that they are alternatives to ZF or ZFC.

2. (music) Musical set theory, a systematic approach to describing musical objects and their relationships.

• sets (informal)

• set-theoretical
• naive set theory

• Appendix:Glossary of set theory