We show that the theory of the partial order of computably enumerable equivalence relations (ceers) under computable reduction is 1-equivalent to true arithmetic. We show the same result for the structure comprised of the dark ceers and the structure comprised of the light ceers. We also show the same for the structure of $\mathcal{I}$-degrees in the dark, light, or complete structure. In each case, we show that there is an interpretable copy of $(\mathbb{N},+,\times )$.

中文翻译：

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核心理论计算真实算术

我们证明了在可计算归约条件下可计算可数等价关系（子）的偏序理论与真实算术是1等效的。对于由深色蜡木组成的结构和由浅蜡木组成的结构，我们显示了相同的结果。我们还显示了相同的结构$\mathcal{一世}$-在黑暗，明亮或完整的结构中度数。在每种情况下，我们都表明存在以下内容的可解释副本：$（\mathbb{ñ}，+，\times ）$。