A note on Humberstone's constant Ω

Satoru Niki,

Hitoshi Omori


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.

AMS subject classification: 03B20, 03B50.

Słowa kluczowe: intuitionistic logic, minimal logic, actuality operator, empirical negation, deduction theorem

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