The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.

Introduction; preliminaries; the nonstationary ideal; the Rho max extension; applications; Rho max variations; conditional variations; principles for Omega 1; extensions of (Gamma, Rho); further results; questions.