Abstract
In the framework of algebras with infinitary operations, the equational theory of \(\bigvee _{\kappa }\)-complete Heyting algebras or Heyting \(\kappa \)-frames is studied. A Hilbert style calculus algebraizable in this class is formulated. Based on the infinitary structure of Heyting \(\kappa \)-frames, an equational type completeness theorem related to the \(\langle \bigvee , \wedge , \rightarrow , 0 \rangle \)-structure of frames is also obtained.
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Acknowledgements
This work is supported by: (1) MIUR project PRIN 2017: “Theory and applications of resource sensitive logics”, CUP: 20173WKCM5; (2) FdS (Fondazione di Sardegna) project “Ubiquitous Quantum Reality (UQR): understanding the natural process under the light of quantum-like structures” (Code: F73C22001360007).
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Freytes, H., Sergioli, G. Heyting \(\kappa \)-Frames. Stud Logica (2023). https://doi.org/10.1007/s11225-023-10072-3
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DOI: https://doi.org/10.1007/s11225-023-10072-3