Monadic k×j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\times j$$\end{document}-rough Heyting algebras [Book Review]

Archive for Mathematical Logic 61 (5-6):611-625 (2021)
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Abstract

In this paper, we introduce the variety of algebras, which we call monadic k×j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\times j$$\end{document}-rough Heyting algebras. These algebras constitute an extension of monadic Heyting algebras and in 3×2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\times 2$$\end{document} case they coincide with monadic 3-valued Łukasiewicz–Moisil algebras. Our main interest is the characterization of simple and subdirectly irreducible monadic k×j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\times j$$\end{document}-rough Heyting algebras. In order to this, an Esakia-style duality for these algebras is developed.

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References found in this work

On monadic MV-algebras.Antonio Di Nola & Revaz Grigolia - 2004 - Annals of Pure and Applied Logic 128 (1-3):125-139.
Algebraic Logic, I. Monadic Boolean Algebras.Paul R. Halmos - 1958 - Journal of Symbolic Logic 23 (2):219-222.
Monadic Distributive Lattices.Aldo Figallo, Inés Pascual & Alicia Ziliani - 2007 - Logic Journal of the IGPL 15 (5-6):535-551.

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