论文标题
连续假设的独立性：直观介绍
Independence of the Continuum Hypothesis: an Intuitive Introduction
论文作者
论文摘要
连续假设的独立性是广泛影响的结果：它解决了关于N和R的性质的一个基本问题，这是两个最熟悉的数学结构。它引入了强迫方法已成为固定理论的主要主力。它对数学基础以及语法与语义的作用具有广泛的影响。尽管其影响很大，但并未广泛教授。主要原因是缺乏对非专业主义者的无障碍博览会，因为证明中使用的数学结构和技术在集合理论之外不熟悉。该手稿旨在通过在高级本科数学家和理论计算机科学家可以访问的水平上提供博览会来解决这一差距，同时涵盖了证明的所有技术挑战性的部分。
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.
