In this paper we review Shelah's strong covering property and its applications. We also extend some of the results of Shelah and Woodin on the failure of equation image by adding a real.

In this paper we study the category of hyper MV-algebras and we prove that it has a terminal object and a coequalizer. We show that Jia's construction can be modified to provide a free hyper MV-algebra by a set. We use this to show that in the category of hyper MV-algebras the monomorphisms are exactly the one-to-one homomorphisms.

In this paper, we consider a collection of filters of a BL-algebra A. We use the concept of congruence relation with respect to filters to construct a uniformity which induces a topology on A. We study the properties of this topology regarding different filters. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim).

In this paper, we consider a collection of filters of a BL-algebra A. We use the concept of congruence relation with respect to filters to construct a uniformity which induces a topology on A. We study the properties of this topology regarding different filters.

In this paper we introduce n -fold implicative basis logic and the related algebras called n -fold implicative BL-algebras. Also we define n -fold implicative filters and we prove some relations between these filters and construct quotient algebras via these filters.