# nLab material set theory

Material set theory

foundations

# Material set theory

## Overview

Material set theory (also called membership-based set theory) is a style of set theory with a primitive global membership relation “$\in$” where sets are characterized only by “$\in$” and propositional equality of sets. (The terminology ‘material’, or at least ‘materialistic’, goes back at least to Friedman 1997.) Material set theory contrasts with structural set theory (cf. material versus structural set theory), as well as with set theories which are neither structural nor material. Material set theories are simply sorted set theory.

## References

Relation to structural set theory is discussed in