L-domains and Lossless Powerdomains

The category of L-domains was discovered by A. Jung while solving the problem of nding maximal cartesian closed categories of algebraic CPO's and continuous functions. In this note we analyse properties of the lossless powerdo-main construction, that is closed on the algebraic L-domains. The powerdomain is shown to be isomorphic to a collection of subsets of the domain on which the construction was done. The proof motivates a certain niteness condition on the inconsistency relations of elements. It is shown that all algebraic CPO's D whose basis B(D) has property M satisfy the condition. In particular, the coherent L-domains satisfy the condition.