Mathematical Logic

Abstract

This paper is the second in a series of three culminating in an ordinal analysis of 2-comprehension. Its objective is to present an ordinal analysis for the subsystem of second order arithmetic with 2-comprehension, bar induction and 1 2-comprehension for formulae without set parameters. Couched in terms of Kripke-Platek set theory, KP, the latter system corresponds to KPi augmented by the assertion that there exists a stable ordinal, where KPi is KP with an additional axiom stating that every set is contained in an admissible set.