\(n\)-fold filters of EQ-algebras

Abstract

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