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On the $\Pi^1_2$ consequences of $\Pi^1_1$-$\mathsf{CA}_0$
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abstract
In this paper, we introduce a hierarchy dividing the set $\{\sigma \in \Pi^1_2 : \Pi^1_1$-$\mathsf{CA}_0 \vdash \sigma\}$. Then, we give some characterizations of this set using weaker variants of some principles equivalent to $\Pi^1_1$-$\mathsf{CA}_0$: leftmost path principle, Ramsey's theorem for $\Sigma^0_n$ classes of $[\mathbb{N}]^{\mathbb{N}}$ and determinacy for $(\Sigma^0_1)_n$ classes of $\mathbb{N}^{\mathbb{N}}$.
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Cited by 1 Pith paper
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On some subtheories of strong dependent choice
The paper characterizes the provable Pi^1_e, Sigma^1_e, and Boolean-combination classes of the strong dependent choice system Sigma^1_i-SDC0 using beta-model reflection principles.
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