Homomorphisms and quotients of degree structures Original Research Article

We investigate homomorphisms of degree structures with various relations, functions and constants. Our main emphasis is on pseudolattices, i.e., partially ordered sets with a join operation and relations simulating the meet operation. We show that there are no finite quotients of the pseudolattice of degrees or of the pseudolattice of degrees ⩽0′, but that many finite distributive lattices are pseudolattice quotients of the pseudolattice of computably enumerable degrees.