In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...

the notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. the extensionproperty for (fuzzy) absorbent orderedfilters is established. conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...

In this paper, we introduce the concept of free abstract fuzzy economy and, using Wu’s existence theorem of maximal elements for lower semicontinuous correspondences [26] and Kim and Lee’s existence theorems of best proximity pairs [14], we prove the existence of fuzzy equilibrium pairs for free abstract fuzzy economies first with upper semicontinuous and then with lower semicontinuous constrai...

Recently Yehuda Rav has given the concept of Semi prime ideals in a general lattice by generalizing the notion of 0-distributive lattices. In this paper we study several properties of these ideals in a general nearlattice and include some of their characterizations. We give some results regarding maximal filters and include a number of Separation properties in a general nearlattice with respect...

We explore the problem of constructing maximal and unbounded filters on computable posets. We obtain both computability results and reverse mathematics results. A maximal filter is one that does not extend to a larger filter. We show that every computable poset has a ∆2 maximal filter, and there is a computable poset with no Π1 or Σ 0 1 maximal filter. There is a computable poset on which every...

We show that the statement CCFC = “the character of a maximal free filter F of closed sets in a T1 space (X, T ) is not countable” is equivalent to the Countable Multiple Choice Axiom CMC and, the axiom of choice AC is equivalent to the statement CFE0 = “closed filters in a T0 space (X, T ) extend to maximal closed filters”. We also show that AC is equivalent to each of the assertions: “every c...