Stationary sets added when forcing squares

Abstract

Current research in set theory raises the possibility that square _{kappa ,<lambda } can be made compatible with some stationary reflection, depending on the parameter lambda . The purpose of this paper is to demonstrate the difficulty in such results. We prove that the poset {mathbb {S}}(kappa ,<lambda ), which adds a square _{kappa ,<lambda }-sequence by initial segments, will also add non-reflecting stationary sets concentrating in any given cofinality below kappa . We also investigate the CMB poset, which adds square _kappa ^* in a slightly different way. We prove that the CMB poset also adds non-reflecting stationary sets, but not necessarily concentrating in any cofinality.