  Just as in set theory, “logical operators” can be defined on the truth-value object in any topos. These are maps ¬: Ω → Ω;  ∧, ∨, ⇒: Ω × Ω → Ω corresponding to the logical operations of negation, conjunction, disjunction and implication. With these operations, Ω becomes a Heyting algebra, thus embodying in general the laws not of classical but of intutionistic logic. In this sense intuitionistic logic is “internalized” in a topos: intuitionistic logic is the logic of variable sets. (Of course, classical logic is internalized in certain toposes, for instance Set and Set(B) for any complete Boolean algebra B.)