A characterization of Stone and linear Heyting algebras

Authors

  • Alejandro Petrovich Departamento de Matem´atica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires
  • Carlos Scirica Escuela de Ciencia y Tecnolog´ıa, Universidad Nacional de San Mart´ın

DOI:

https://doi.org/10.33044/revuma.2052

Abstract

An important problem in the variety of Heyting algebras $\mathcal{H}$ is to find new characterizations which allow us to determinate if a given $H\in \mathcal{H}$ is linear or Stone. In this work we present two Heyting algebras, $H^{ns}$ and $H^{snl}$, such that: (a) a Heyting algebra $H$ is a Stone–Heyting algebra if and only if $H^{ns}$ cannot be embedded in $H$, and (b) $H$ is a linear Heyting algebra if and only if neither $H^{ns}$ nor $H^{snl}$ can be embedded in $H$.

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References

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Published

2022-04-18

Issue

Vol. 63 No. 1 (2022)

Section

Article

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Copyright (c) 2022 Alejandro Petrovich, Carlos Scirica

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