Heyting κ -Frames

In the framework of algebras with infinitary operations, the equational theory of ⋁ _κ -complete Heyting algebras or Heyting κ -frames is studied. A Hilbert style calculus algebraizable in this class is formulated. Based on the infinitary structure of Heyting κ -frames, an equational type completeness theorem related to the ⟨⋁ , ∧ , → , 0 ⟩ -structure of frames is also obtained.