- 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).
- Musical set theory may be considered the application of mathematical set theory to music.