Semilattices, Domains, and Computability (Invited Talk)

Dana Scott
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 lattice form a semilattice (under join). This semilattice has a zero element, and,...