Maximal subalgebras of Heyting algebras

A Heyting algebra is an algebra H ;∨,∧ →, 0,1) of type (2,2,2,0,0) for which H ;∨,∧,0,1) is a bounded distributive lattice and → is the binary operation of relative pseudocomplementation (i.e., for a,b,c ∈ H , a c ∧≦ b irr c ≦ a → b ). Associated with every subalgebra of a Heyting algebra is a separating set. Those corresponding to maximal subalgebras are characterized in Proposition 8 and, subsequently, are used in an investigation of Heyting algebras.