Fatal Heyting Algebras and Forcing Persistent Sentences

摘要

Hamkins and L?we 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.