Square and Delta reflection

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

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