Heyting $$\kappa $$-Frames
Héctor Freytes, Giuseppe Sergioli · Studia Logica · 2023
Abstract In the framework of algebras with infinitary operations, the equational theory of $$\bigvee _{\kappa }$$ ⋁ κ -complete Heyting algebras or Heyting $$\kappa $$ κ -frames is studied. A Hilbert style calculus algebraizable in this class is formulated. Based on the infinitary structure of Heyting $$\kappa $$ κ -frames, an equational type completeness theorem related to the $$\langle \bigvee , \wedge , \rightarrow , 0 \rangle $$ ⟨ ⋁ , ∧ , → , 0 ⟩ -structure of frames is also obtained.