论文标题
通过猜测模型通往紧凑的道路
A Road To Compactness Through Guessing Models
论文作者
论文摘要
紧凑型现象是数学中结构主义的特色方面之一。简而言之，如果相关属性通过该结构的许多下结构满足，则紧凑型属性在结构中存在。有了这种现象及其双胞胎兄弟姐妹的“反思”，现代集合理论解决了许多数学陈述，并没有被传统上接受的数学形式主义（$ \ rm ZFC $）所确定。一项广泛的研究计划调查了紧凑的概念是否可以在不遇到矛盾的情况下出现宇宙。 这些笔记是一项关于猜测模型的调查，其存在提供了令人着迷的紧凑现象。手稿中的大多数结果都是众所周知的。我们将重新制定，推广和扩展其中的一些。我们还提出了一些猜测模型的已知应用，并提出了一些开放问题。
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that structure. With this phenomenon and its twin sibling "reflection", modern set theory has settled many mathematical statements left undecided by the conventionally accepted formalism of mathematics, $\rm ZFC$. A broad research program investigates whether a notion of compactness can universe-widely emerge without running into contradictions. These notes are a survey about guessing models whose existence provides intriguing compactness phenomena. Most of the results in the manuscript are well-known. We shall reformulate, generalise and expand some of them. We also present some known applications of guessing models and state some open problems.
