The 0-distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for 0-distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.

We deene conndence relations on Boolean lattices, which can be interpreted as ordinal representations of uncertainty or information. The set of the conndence relations on a given Boolean lattice can be ordered by set inclusion and thus is shown to form a complete meet-semilattice. We investigate and identify the maximal elements of this structure. Moreover, we prove that it is in particular an ...

We study computably enumerable equivalence relations (ceers), under the reducibility R ≤ S if there exists a computable function f such that x R y if and only if f(x) S f(y), for every x, y. We show that the degrees of ceers under the equivalence relation generated by ≤ form a bounded poset that is neither a lower semilattice, nor an upper semilattice, and its first order theory is undecidable....

We define confidence relations on Boolean lattices, which can be interpreted as ordinal representations of uncertainty or information. The set of the confidence relations on a given Boolean lattice can be ordered by set inclusion and thus is shown to form a complete meet-semilattice. We investigate and identify the maximal elements of this structure. Moreover, we prove that it is in particular ...

Weak relative pseudocomplementation on a meet semilattice S is a partial operation ∗ which associates with every pair (x, y) of elements, where x ≥ y, an element z (the weak pseudocomplement of x relative to y) which is the greatest among elements u such that y = u ∧ x. The element z coincides with the pseudocomplement of x in the upper section [y) and, if S is modular, with the pseudocomplemen...

We study how the existence in an algebraic lattice L of a chain of a given type is reflected in the join-semilattice K(L) of its compact elements. We show that for every chain α of size κ, there is a set B of at most 2 join-semilattices, each one having a least element such that an algebraic lattice L contains no chain of order type I(α) if and only if the join-semilattice K(L) of its compact e...

Weak relative pseudocomplementation on a meet semilattice S is a partial operation ∗ which associates with every pair (x, y) of elements, where x ≥ y, an element z (the weak pseudocomplement of x relative to y) which is the greatest among elements u such that y = u ∧ x. The element z coincides with the pseudocomplement of x in the upper section [y) and, if S is modular, with the pseudocomplemen...