Heyting $$\kappa $$-Frames

Freytes, Hector;Sergioli, Giuseppe

2024-01-01

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Abstract

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.