Axiom of Extensionality
The Axiom of Extensionality is a possible axiom in Material set theory that seems to follow directly from Cantor's definition of the set: #m/def/set/zf
which is to say, two sets are the same iff they have the same elements.
Relation to other axioms
- The Axiom of Extensionality seems to give a complete definition of set equality, but if we are dealing with ill-founded sets it may reduce to tautologous
Axiom of Extensionality for classes
In a material set theory with classes have an identical axiom with sethood replaced with classhood: #m/def/set/nbg
#state/tidy | #lang/en | #SemBr