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Is there a $\Pi_2$ sentence $A$ such that $\text{ZFC}^- + A$ proves powerset?
No, using downward Löwenheim-Skolem theorem (and transitive collapses), every true $Π_2$ statement holds in $H(λ)$ for every cardinal $λ>ω$. ($H(λ)$ consists of all sets whose transitive closure ...
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