Abstract

The paper contains some observations on e-complete, precomplete, and uniformly finitely precomplete r. e. equivalence relations. Among these are a construction of a uniformly finitely precomplete r. e. equivalence which is neither e- nor precomplete, an extension of Lachlan's theorem that all precomplete r. e. equivalences are isomorphic, and a characterization of sets of fixed points of endomorphisms of uniformly finitely precomplete r. e. equivalences.