Fatal Heyting Algebras and Forcing Persistent Sentences
Leo Esakia, Benedikt Löwe

Abstract:
Hamkins and Löwe proved that the modal logic of forcing is S4.2. In
this paper, we consider its modal companion, the intermediate logic KC
and relate it to the fatal Heyting algebra H_ZFC of forcing persistent
sentences. This Heyting algebra is equationally generic for the class
of fatal Heyting algebras. Motivated by these results, we further
analyse the class of fatal Heyting algebras.