It was recently shown by Atserias, Buss and Mueller that the standard complexity-theoretic conjecture NEXP not in P / poly is consistent with the relatively strong bounded arithmetic theory V^0_2, which can prove a substantial part of complexity theory. We observe that their approach can be extended to show that the stronger conjectures NEXP not in EXP / poly and NEXP not in coNEXP are consistent with a stronger theory, which includes every true universal number-sort sentence.

翻译：Atserias、Buss和Mueller近期证明，标准复杂性理论猜想NEXP不在P/poly中，与相对强的有界算术理论V^0_2是一致的，该理论可证明复杂性理论的实质性部分。我们指出，他们的方法可扩展以证明更强的猜想——NEXP不在EXP/poly中以及NEXP不在coNEXP中——与一个更强的理论是一致的，该理论包含所有真的一阶数论全称语句。