How strong is $\Sigma^1_n \textrm{-DC}_0$ in terms of consistency strength? I know it is conservative to $\Pi^1_n \textrm{-TI}_0$, but I don't know its relation to other subsystems. Are there any other subsystems of $Z_2$ which $\Sigma^1_n \textrm{-DC}_0$ is conservative over? If not, does anybody know upper and lower bounds better than "in-between $\textrm{ACA}_0$ and $\textrm{ATR}_0$"? Thanks.
2026-03-25 18:48:12.1774464492
Strength and conservativity of $\Sigma^1_n \textrm{-DC}_0$
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