\(n\)-Fold Filters of EQ-Algebras

Authors

DOI:

https://doi.org/10.18778/0138-0680.2022.09

Keywords:

\(EQ\)-algebra, \(n\)-fold pseudo implicative (implicative, obstinate, fantastic) prefilter, \(n\)-fold pseudo implicative (implicative, fantastic) EQ-algebra

Abstract

In this paper, we apply the notion of \(n\)-fold filters to the \(EQ\)-algebras and introduce the concepts of \(n\)-fold pseudo implicative, \(n\)-fold implicative, \(n\)-fold obstinate, \(n\)-fold fantastic prefilters and filters on an \(EQ\)-algebra \(\mathcal{E}\). Then we investigate some properties and relations among them. We prove that the quotient algebra \(\mathcal{E}/F\) modulo an 1-fold pseudo implicative filter of an \(EQ\)-algebra \(\mathcal{E}\) is a good \(EQ\)-algebra and the quotient algebra \(\mathcal{E}/F\) modulo an 1-fold fantastic filter of a good \(EQ\)-algebra \(\mathcal{E}\) is an \(IEQ\)-algebra.

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Published

2022-10-14

How to Cite

Ganji Saffar, B., Kologani, M. A., & Borzooei, R. A. (2022). \(n\)-Fold Filters of EQ-Algebras. Bulletin of the Section of Logic, 51(4), 455–486. https://doi.org/10.18778/0138-0680.2022.09

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Research Article

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