The importance of being discrete
Balder ten Cate, Tadeusz Litak

Abstract:
The paper discusses discrete frames as an attractive semantics for
modal logic. We study questions of completeness, persistence, duality
and definability. Notions of completeness, strong global completeness
and complexity of dual varieties coincide for discrete frames;
moreover, they are equivalent to conservativity of minimal hybrid
extensions. The paper also provides some criteria of di-persistence
and a Goldblatt-Thomason theorem for discrete frames.