We analyse Kreisel's notion of human-effective computability. Like Kreisel, we relate this notion to a concept of informal provability, but we disagree with Kreisel about the precise way in which this is best done. The resulting two different ways of analysing human-effective computability give rise to two different variants of Church's thesis. These are both investigated by relating them to transfinite progressions of formal theories in the sense of Feferman.

中文翻译：

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人类有效的可计算性†

我们分析了 Kreisel 的人类有效可计算性概念。像 Kreisel 一样，我们将这个概念与非正式可证明性的概念联系起来，但我们不同意 Kreisel 的最佳方式。由此产生的两种不同的分析人类有效可计算性的方法导致了丘奇论文的两种不同变体。这些都是通过将它们与 Feferman 意义上的形式理论的超限级数相关联来研究的。