A note on Humberstone's constant Ω
Satoru Niki, Hitoshi Omori · Reports on Mathematical Logic · 2021
We investigate an expansion of positive intuitionistic logic obtained by adding a constant Ω introduced by Lloyd Humberstone. Our main results include a sound and strongly complete axiomatization, some comparisons to other expansions of intuitionistic logic obtained by adding actuality and empirical negation, and an algebraic semantics. We also brie y discuss its connection to classical logic.