Let S, T be semilattices. Let us assume that if S is upper-bounded, then T is upper-bounded. A map from S into T is said to be a semilattice morphism from S into T if: (Def. 1) For every finite subset X of S holds it preserves inf of X . Let S, T be semilattices. Observe that every map from S into T which is meet-preserving is also monotone. Let S be a semilattice and let T be an upper-bounded ...

Considering the lattice of properties of a physical system, it has been argued elsewhere that – to build a calculus of propositions having a well-behaved notion of disjunction (and implication) – one should consider a very particular frame completion of this lattice. We show that the pertinent frame completion is obtained as sheafification of the presheaves on the given meet-semilattice with re...

The Alexander dual of an arbitrary meet-semilattice is described explicitly. Meet-distributive meet-semilattices whose Alexander dual is level are characterized.

Let S, T be semilattices. Let us assume that if S is upper-bounded, then T is upper-bounded. A map from S into T is said to be a semilattice morphism from S into T if: (Def. 1) For every finite subset X of S holds it preserves inf of X. Let S, T be semilattices. One can check that every map from S into T which is meet-preserving is also monotone. Let S be a semilattice and let T be an upper-bou...

We study the stability and the stability index of themeet game form defined on a meet-semilattice. Given any active coalition structure, we show that the stability index relative to the equilibrium, to the beta core and to the exact core is a function of the Nakamura number, the depth of the semilattice and its gap function.

A nearlattice is a meet semilattice A in which every initial segment Ap := {x : x ≤ p} happens to be a join semilattice (hence, a lattice) with respect to the natural ordering of A. If all lattices Ap are distributive, the nearlattice itself is said to be distributive. It is known that a distributive nearlattice can be represented as a nearlattice of sets. We call an algebra (A,∧,∨) of type (2,...

1. Introduction. A meet semilattice is said to be weakly relatively pseudocomplemented, or just wr-pseudocomplemented, if, for every element x and every y ≤ x, all the maxima