A New Extended Soft Intersection Set to M

Molodtsov’s soft set theory provides a general mathematical framework for dealing with uncertainty. The concepts of (M,N)-SI implicative (Boolean) filters of BL-algebras are introduced. Some good examples are explored. The relationships between (M,N)-SI filters and (M,N)-SI implicative filters are discussed. Some properties of (M,N)-SI implicative (Boolean) filters are investigated. In particular, we show that (M,N)-SI implicative filters and (M,N)-SI Boolean filters are equivalent

Characterizations of Some Fuzzy Prefilters (Filters) in E

We introduce and study some types of fuzzy prefilters (filters) in EQ-algebras. First, we present several characterizations of fuzzy positive implicative prefilters (filters), fuzzy implicative prefilters (filters), and fuzzy fantastic prefilters (filters). Next, using their characterizations, we mainly consider the relationships among these special fuzzy filters. Particularly, we find some conditions under which a fuzzy implicative prefilter (filter) is equivalent to a fuzzy positive implicative prefilter (filter). As applications, we obtain some new results about classical filters in EQ-algebras and some related results about fuzzy filters in residuated lattices

Characteristic formulas over intermediate logics

We expand the notion of characteristic formula to infinite finitely presentable subdirectly irreducible algebras. We prove that there is a continuum of varieties of Heyting algebras containing infinite finitely presentable subdirectly irreducible algebras. Moreover, we prove that there is a continuum of intermediate logics that can be axiomatized by characteristic formulas of infinite algebras while they are not axiomatizable by standard Jankov formulas. We give the examples of intermediate logics that are not axiomatizable by characteristic formulas of infinite algebras. Also, using the Goedel-McKinsey-Tarski translation we extend these results to the varieties of interior algebras and normal extensions of S