Square and Delta reflection

Starting from infinitely many supercompact cardinals, we force a model of ZFC where ℵω2+1ℵω2+1 satisfies simultaneously a strong principle of reflection, called Δ-reflection, and a version of the square principle, denoted □(ℵω2+1)□(ℵω2+1). Thus we show that ℵω2+1ℵω2+1 can satisfy simultaneously a strong reflection principle and an anti-reflection principle.