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Characterizations of near-Heyting algebras

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Abstract

A near-Heyting algebra is a join-semilattice with a greatest element such that every principal upset is a Heyting algebra. We will present several characterizations of the concept of near-Heyting algebra. We will show that the class of near-Heyting algebras is a subclass of Hilbert algebras with supremum. We introduce prelinear near-Heyting algebras and present some of their characterizations.

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Acknowledgements

We would like to thank the anonymous referee for his/her valuable comments and suggestions that helped to improve the present paper.

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Authors and Affiliations

  1. Facultad de Ciencias Exactas y Naturales, Universidad Nacional de La Pampa, 6300, Santa Rosa, La Pampa, Argentina

    Luciano J. González & Marina B. Lattanzi

  2. CIC and Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional del Centro de la Provincia de Buenos Aires, 7000, Tandil, Buenos Aires, Argentina

    Ismael Calomino & Sergio A. Celani

Authors
  1. Luciano J. González
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  2. Marina B. Lattanzi
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  3. Ismael Calomino
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  4. Sergio A. Celani
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Correspondence to Luciano J. González.

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González, L.J., Lattanzi, M.B., Calomino, I. et al. Characterizations of near-Heyting algebras. European Journal of Mathematics 9, 68 (2023). https://doi.org/10.1007/s40879-023-00663-8

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  • DOI: https://doi.org/10.1007/s40879-023-00663-8

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