We have previously established that [Formula: see text]-comprehension is equivalent to the statement that every dilator has a well-founded Bachmann–Howard fixed point, over [Formula: see text]. In this paper, we show that the base theory can be lowered to [Formula: see text]. We also show that the minimal Bachmann–Howard fixed point of a dilator [Formula: see text] can be represented by a notation system [Formula: see text], which is computable relative to [Formula: see text]. The statement that [Formula: see text] is well founded for any dilator [Formula: see text] will still be equivalent to [Formula: see text]-comprehension. Thus, the latter is split into the computable transformation [Formula: see text] and a statement about the preservation of well-foundedness, over a system of computable mathematics.

中文翻译：

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巴赫曼-霍华德原理的可计算方面

我们之前已经确定[公式：见文本]-理解等价于每个扩张器在[公式：见文本]上都有一个有根据的巴赫曼-霍华德不动点的陈述。在本文中，我们展示了基础理论可以简化为[公式：见正文]。我们还表明，扩张器 [公式：见文本] 的最小 Bachmann-Howard 不动点可以用符号系统 [公式：见文本] 表示，该符号系统相对于 [公式：见文本] 是可计算的。[公式：见文本]对于任何扩张器[公式：见文本]的陈述仍然等同于[公式：见文本]-理解。因此，后者被分为可计算变换[公式：见正文]和关于在可计算数学系统上保持有根据的陈述。