# Set theory

**Set theory**is the mathematical theory of sets, which represent collections of abstract objects. It has a central role in modern mathematical theory, providing the basic language in which most of mathematics is expressed.

For more information on set theory in Wikipedia, see:

- Naive set theory is the original set theory developed by mathematicians at the end of the 19th century
- Axiomatic set theory is a rigorous axiomatic theory developed in response to the discovery of serious flaws (such as Russell's Paradox) in naive set theory.
- Various versions of logic have associated sorts of sets (such as fuzzy sets in fuzzy logic).
- Internal set theory
- Musical set theory may be considered the application of mathematical set theory to music.