From what I can tell, every lattice is a sublattice of a lattice with unique complements (Dilworth). A Heyting algebra is a distributive lattice. The only remaining step, then, would be to know whether the extension with unique complements preserves distributivity. If that is true, then every Heyting algebra would be a sublattice of a distributive complemented lattice, a Boolean algebra.
2026-02-23 06:59:33.1771829973
Is every Heyting algebra a sublattice of a Boolean algebra?
161 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
2
Every distributive lattice is isomorphic to a lattice of sets, so in particular it is a sublattice of a Boolean algebra. Since Heyting algebras are distributive lattices, the answer to your question is affirmative.