Abstract
These notes were written by Abraham Robinson in preparation for his paper with Peter Roquette [4]. They were written shortly before his death in 1974, but were omitted from the published paper. The published material was in much more polished, and use different terminology. Nevertheless these notes are easily understood with a knowledge of [4]. What Robinson aimed at in those notes was done by number-theoretical methods in [6]. See also [5] for the logical side of the subject.
In those notes, Robinson used the elementary and familiar idea that consequence relative to nonstandard models is recursively enumerable in the set of axioms defining the class. The idea is intriguing because nonstandard models are usually associated with very nonconstructive ideas especially, because the models needed cannot be recursive. These notes should be a useful reminder for applications of the idea in nonstandard mathematics. (G.T.)
