set theory

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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, page 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”, in Dov M. Gabbay, Akihiro Kanimori, John Woods, editors, Sets and Extensions in the Twentieth Century, North-Holland: Elsevier, 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-theoretic, set-theoretical, set-theoretically
• naive set theory
• Zermelo set theory
• Zermelo-Fraenkel set theory

• Appendix:Glossary of set theory