Not Every Splitting Heyting or Interior Algebra is Finitely Presentable

Studia Logica 100 (1-2):115-135 (2012)
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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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10.1007/s11225-012-9391-1

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Citations of this work

The Admissible Rules of ${{mathsf{BD}_{2}}}$ and ${mathsf{GSc}}$.Jeroen P. Goudsmit - 2018 - Notre Dame Journal of Formal Logic 59 (3):325-353.

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References found in this work

Modal logic.Alexander Chagrov - 1997 - New York: Oxford University Press. Edited by Michael Zakharyaschev.
On Intermediate Propositional Logics.Toshio Umezawa - 1968 - Journal of Symbolic Logic 33 (4):607-607.
Intermediate logics and the disjunction property I.Andrzej Wronski - 1972 - Bulletin of the Section of Logic 1 (4):46-53.

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