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.
Heyting $$\kappa $$-Frames
Freytes, Hector;Sergioli, Giuseppe
2023-01-01
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.
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