Entailment in propositional Godel logics can be defined in a natural way: While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ; it is shown that there is a rich structure of infinite-valued Godel logics, only one of which is compact, it is also shown that The compact infinite-valued Godel logic is the only one which interpolates, and the only one with an r.e, entailment relation.