Square and Delta reflection

Abstract

Starting from infinitely many supercompact cardinals, we force a model of ZFC where ${\aleph }_{{\omega }^2+1}$ satisfies simultaneously a strong principle of reflection, called $\Delta$-reflection, and a version of the square principle, denoted $\square ({\aleph }_{{\omega }^2+1}).$ Thus we show that ${\aleph }_{{\omega }^2+1}$ can satisfy simultaneously a strong reflection principle and an anti-reflection principle.