The Mostowski Bridge

In 1950, Novak and Mostowski showed that GB (Gödel-Bernays theory of classes) is conservative over ZF, and therefore by Gödel's second incompleteness theorem the consistency of ZF is unprovable in GB. In the same year Mostowski unveiled a contrasting result: GB provides a truth-definition for ZF-formulae. Here we first give an expository account of Mostowski's construction and surrounding results, and then we show that the construction bridges the domain of Tarski-style truth theories over PA with certain subsystems of second order arithmetic.