The aim of this paper is to give a new equivalent set of axioms for MV-algebras, and to show that the axioms are independent. In addition to this, we handle Yang-Baxter equation problem. In conclusion, we construct a new set-theoretical solution for the Yang-Baxter equation by using MV-algebras.
Abstract:In this study, a term operation Sheffer stroke is presented in a given basic algebra A and the properties of the Sheffer stroke reduct of A are examined. In addition, we qualify such Sheffer stroke basic algebras. Finally, we construct a bridge between Sheffer stroke basic algebras and Boolean algebras.
The aim of this study is to introduce fuzzy filters of Sheffer stroke Hilbert algebra. After defining fuzzy filters of Sheffer stroke Hilbert algebra, it is shown that a quotient structure of this algebra is described by its fuzzy filter. In addition to this, the level filter of a Sheffer stroke Hilbert algebra is determined by its fuzzy filter. Some fuzzy filters of a Sheffer stroke Hilbert algebra are defined by a homomorphism. Normal and maximal fuzzy filters of a Sheffer stroke Hilbert algebra and the relation between them are presented. By giving the Cartesian product of fuzzy filters of a Sheffer stroke Hilbert algebra, various properties are examined.
Abstract:In this work, we introduce Wajsberg algebras which are equivalent structures to MV-algebras in their implicational version, and then we define new notions and give new solutions to the set-theoretical Yang-Baxter equation by using Wajsberg algebras.
Our investigation is concerned with the finite model property (fmp) with respect to admissible rules. We establish general sufficient conditions for absence of frnp w. I. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic X containing K4 with the co-cover property and of width > 2 has fmp w. I. t . admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem -K4 itself, S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp -the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width 5 2, there exists a zone for fmp w. r. t. admissibility. It is shown (Theorem 4.3) that all modal logics X of width 5 2 extending S4 which are not sub-logics of three special tabular logics (which is equipotent to all these X extend a certain subframe logic defined over S4 by omission of four special frames) have fmp w. I. t. admissibility.Mathematics Subject Classification: 03B45, 03F07.
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