论文标题
俱乐部猜测工具箱我
A club guessing toolbox I
论文作者
论文摘要
谢拉（Shelah）引入了俱乐部的猜测原则，以减弱詹森的钻石。最令人叹为观止的是，它们被用来证明Shelah的ZFC在第一个奇异红衣主教的力量上绑定。 这些原则发现了许多其他应用：在基本算术和PCF理论中；在不可数的枢机主教上的组合物体（例如琼斯森代数，浓烈的颜色，苏斯林树和病理图）上的结构中；在模型理论中普遍不存在；不存在强迫公理在较高的不可数的红衣主教处；还有更多。 在本系列的第一部分中，我们调查了文献中出现的各种形式的俱乐部猜测，然后系统地研究了可以改善俱乐部猜测序列的各种方式，尤其是在猜测频率的方式中。 我们包括一个用于俱乐部猜测的人的说明部分，可以独立于本文的其余部分阅读。
Club guessing principles were introduced by Shelah as a weakening of Jensen's diamond. Most spectacularly, they were used to prove Shelah's ZFC bound on the power of the first singular cardinal. These principles have found many other applications: in cardinal arithmetic and PCF theory; in the construction of combinatorial objects on uncountable cardinals such as Jonsson algebras, strong colourings, Souslin trees, and pathological graphs; to the non-existence of universals in model theory; to the non-existence of forcing axioms at higher uncountable cardinals; and many more. In this paper, the first part of a series, we survey various forms of club-guessing that have appeared in the literature, and then systematically study the various ways in which a club-guessing sequences can be improved, especially in the way the frequency of guessing is calibrated. We include an expository section intended for those unfamiliar with club-guessing and which can be read independently of the rest of the article.
