连续假设独立:直觉导言 (Independence of the Continuum Hypothesis: an Intuitive Introduction)

from arxiv, - Edited the example in the Reflection definition. - Changed fonts for rank() and nr() - Changed fonts for CH to \mathrm{CH} - Corrected a few spurious typos

The independence of the continuum hypothesis is a result of broad impact: it settles a basic question regarding the nature of N and R, two of the most familiar mathematical structures; it introduces the method of forcing that has become the main workhorse of set theory; and it has broad implications on mathematical foundations and on the role of syntax versus semantics. Despite its broad impact, it is not broadly taught. A main reason is the lack of accessible expositions for nonspecialists, because the mathematical structures and techniques employed in the proof are unfamiliar outside of set theory. This manuscript aims to take a step in addressing this gap by providing an exposition at a level accessible to advanced undergraduate mathematicians and theoretical computer scientists, while covering all the technically challenging parts of the proof.

翻译：连续假设的独立性是广泛影响的结果:它解决了N和R这两个最熟悉的数学结构中两个最熟悉的数学结构的性质的基本问题;它引入了已成为既定理论主要工作马的强迫方法;它对于数学基础和语法与语义的作用具有广泛的影响;尽管它具有广泛的影响,但它没有被广泛教授;一个主要原因是非专家缺乏无障碍的解说,因为证据中使用的数学结构和技术在既定理论之外是不熟悉的。这份手稿的目的是通过在高级本科生数学家和理论计算机科学家可以进入的层次上进行解说,同时涵盖证据中技术上具有挑战性的所有部分,从而在弥补这一差距方面迈出一步。