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arXiv · 2411.17415

On some subtheories of strong dependent choice

Juan P. Aguilera·Yudai Suzuki·Keita Yokoyama
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Abstract

In this paper, we give characterizations of the set of $\Pi^1_{e}$-consequences, $\Sigma^1_{e}$-consequences and $\mathsf{B}(\Pi^1_{e})$-consequences of the axiomatic system of the strong dependent choice for $\Sigma^1_i$ formulas $\Sigma^1_i$-$\mathsf{SDC}_0$ for $i > 0$ and $e < i+2$. Here, $\mathsf{B}(\Gamma)$ denotes the set generated by $\land,\lor,\lnot$ starting from $\Gamma$.

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Juan P. Aguilera, Yudai Suzuki, Keita Yokoyama. 2024-11-26. On some subtheories of strong dependent choice. https://arxiv.org/abs/2411.17415

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