Incompatibility of Generic Hugeness Principles

Abstract

We show that the weakest versions of Foreman's minimal generic hugeness axioms cannot hold simultaneously on adjacent cardinals. Moreover, conventional forcing techniques cannot produce a model of one of these axioms.The author wishes to thank the Austrian Science Fund (FWF) for the generous support through grants P34603 and START Y1012-N35 (PI: Vera Fischer).1 This is a ``preproof'' accepted article for The Bulletin of Symbolic Logic. This version may be subject to change during the production process.