Abstract
We give an example of a variety of Heyting algebras and of a splitting algebra in this variety that is not finitely presentable. Moreover, we show that the corresponding splitting pair cannot be defined by any finitely presentable algebra. Also, using the Gödel-McKinsey-Tarski translation and the Blok-Esakia theorem, we construct a variety of Grzegorczyk algebras with similar properties.
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In memoriam of Leo Esakia
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Citkin, A. Not Every Splitting Heyting or Interior Algebra is Finitely Presentable. Stud Logica 100, 115–135 (2012). https://doi.org/10.1007/s11225-012-9391-1
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DOI: https://doi.org/10.1007/s11225-012-9391-1