The Barwise-Schlipf theorem.

In 1975 Barwise and Schlipf published a landmark paper whose main theorem asserts that a nonstandard model M of PA (Peano arithmetic) is recursively saturated iff M has an expansion that satisfies the subsystem Δ11−CA0 of second order arithmetic. In this paper we identify a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, and we offer a correct proof of the problematic direction. [ABSTRACT FROM AUTHOR]