大家好，我是大老李。今天节目主题是“帕里斯-哈林顿”定理(Paris-Harrington)，这个定理是有关不可证明的命题的。说到不可证明的命题，大家第一感觉一定是连续统假设。那这个帕里斯哈-林顿定理为啥也重要呢？我们先要搞清楚什么是不可证明性。第一季节目里我有一期节目是哥德尔不完备性原理。我们简单复习一下。哥德尔的第一不完备原理是说对任何包含皮亚诺算术且可以公理化的理论，这个理论是不完全的。不完全的意思就是这个系统内存在既不能证明也不能证伪的命题。连续统假设就是这样一个命题。但这里面提到皮亚诺算术，这是什么东西呢？不久前的一期节目我们聊到过策梅洛-弗兰克尔的公理化集合论，简称ZFC系统。那套集合论其实是定义了一套有关集合的公理，使用这套公理，你可以知道哪些逻辑推理方法是可以用的。但是只有逻辑推理，没有推理的源头，还是推不出数学。加强的有穷拉姆齐定理：
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