A new characterization of complete Heyting and co-Heyting algebras

摘要

We give a new order-theoretic characterization of a complete Heyting andco-Heyting algebra $C$. This result provides an unexpected relationship withthe field of Nash equilibria, being based on the so-called Veinott orderingrelation on subcomplete sublattices of $C$, which is crucially used in Topkis'theorem for studying the order-theoretic stucture of Nash equilibria ofsupermodular games.