Forcing a set model of Z(3) + Harrington's Principle

摘要

Let Z(3) denote third order arithmetic. Let Harrington's Principle, HP, denote the statement that there is a real x such that every x-admissible ordinal is a cardinal in L. In this paper, assuming there exists a remarkable cardinal with a weakly inaccessible cardinal above it, we force a set model of Z(3) + HP via set forcing without reshaping. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim