Initial segments of the degrees of constructibility (Q1109767)

This paper defines the notion of (countable) algebraic lattices; as a special case, well founded lattices or complete linear orderings are algebraic. It is shown that for every constructible countable algebraic lattice \({\mathcal L}\) there is a generic extension M of L (the constructible universe) such that the degrees of constructibility of the reals in M form a lattice isomorphic to \({\mathcal L}\). Examples are given of complete but non-algebraic lattices which cannot be realized in this way.