As everyone knows, one popular notion of Scott domain is defined as a bounded complete algebraic cpo. These are closely related to algebraic lattices: (i) A Scott domain becomes an algebraic lattice with the adjunction of an (isolated) top element. (ii) Every non-empty Scott-closed subset of an algebraic lattice is a Scott domain. Moreover, the isolated (= compact) elements of an algebraic latt...

A semilattice decomposition of an inverse semigroup has good internal mapping properties. These are used to give natural proofs of some embedding theorems, which were originally proved in a rather artificial way. The reader is referred to [1] for the basic theory of inverse semigroups. In an earlier paper [3] we proved the following embedding result: (1) An E-unitary inverse semigroup is isomor...

Abstract For a Hausdorff topologized semilattice X its Lawson number $$\bar{\Lambda }(X)$$ Λ ¯ ( X ) is the smallest cardinal $$\kappa $$ κ such that for any distinct points $$x...

The application of ideas from universal algebra to computer science has long been a major theme of Joseph Goguen’s research, perhaps even the major theme. One strand of this work concerns algebraic datatypes. Recently there has been some interest in what one may call algebraic computation types. As we will show, these are also given by equational theories, if one only understands the notion of ...