Material set theory

Axiom of Purity

The Axiom of Purity is a possible axiom of material set theory included in most axiomatizations of : #m/def/set

which is to say, the domain of discourse is restricted to sets, and thus every set is a pure set and there are no urelements. Usually, purity is not taken as an axiom and instead everything in the universe is implicitly taken to be a set, doing away with the sethood predicate . Since many axioms of material set theory must be modified to allow for urelements, these notes will not assume purity instead opting to treat it as a separate, optional axiom.

#state/tidy | #lang/en | #SemBr