MacNeile Completions of Heyting Algebras
Guram Bezhanishvil, John Harding · Houston journal of mathematics · 2004
In this note we provide a topological description of the MacNeille completion of a Heyting algebra similar to the description of the MacNeille completion of a Boolean algebra in terms of regular open sets of its Stone space. We also show that the only varieties of Heyting algebras that are closed under MacNeille completions are the trivial variety, the variety of all Boolean algebras, and the variety of all Heyting algebras.