nLab material set theory

Material set theory




The basis of it all

 Set theory

set theory

Foundational axioms

foundational axioms

Removing axioms

Material set theory


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.


Relation to structural set theory is discussed in

See also

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