Representability in lambda algebras

Summary § 1 is concerned with the term model of the α-calculus. It is proved that Church's δ is not dofinable and that the definable functions into the numerals are constant. In § 2 it is proved that for several α-algebras the range of a representable function is either a singleton or infinite. In § 3 it is examined in which α-algebras the local representability of external functions implies the global representability.