We consider the lower semilattice D of diierences of c.e. sets under inclusion. It is shown that D is not distributive as a semilattice, and that the c.e. sets form a deenable subclass.

Recent results of Bucciarelli show that the semilattice of degrees of parallelism of firstorder boolean functions in PCF has both infinite chains and infinite antichains. By considering a simple subclass of Sieber’s sequentiality relations, we identify levels in the semilattice and derive inexpressibility results concerning functions on different levels. This allows us to further explore the st...

We place ourselves in a so-called meet-closed description context; that is a context consisting of a finite nonempty entity set E whose elements are described in a complete meet-semilattice D, by means of a descriptor δ. Then we consider multiway quasi-ultrametric dissimilarities on E, a class of multiway dissimilarities that, with their relative k-balls, extend the fundamental in classificatio...

We show that a locally finite variety which omits abelian types is self–rectangulating if and only if it has a compatible semilattice term operation. Such varieties must have type–set {5 }. These varieties are residually small and, when they are finitely generated, they have definable principal congruences. We show that idempotent varieties with a compatible semilattice term operation have the ...

A specialization semilattice is a join together with coarser preorder $ \sqsubseteq satisfying an appropriate compatibility condition. If $X$ topological space, then $(\mathcal P(X), \cup, )$ semilattice, where x y$ if $x \subseteq Ky$, for $x,y X$, and $K$ closure. Specialization semilattices posets appear as auxiliary structures in many disparate scientific fields, even unrelated to topology....

In this paper, we study structures such as distributive lattices, semilattices, and median graphs from an algorithmic point of view. Such are very useful in classification phylogeny for representing lineage relationships example. A lattice can be considered a graph while ∨-semilattice provided that some conditions holding on triple elements satisfied. Starting structure with different represent...

For any amalgam (S, T; U) of inverse semigroups, it is shown that the natural partial order on S *u T, the (inverse semigroup) free product of S and T amalgamating U, has a simple form onSUT. In particular, it follows that the semilattice of 5 *u T is a bundled semilattice of the corresponding semilattice amalgam (E(S), E(T); E(U)); taken jointly with a result of Teruo Imaoka, this gives that t...