乌拉姆说得对吗？第一章：基本理论与次正规理想
Was Ulam right? I: Basic theory and subnormal ideals
摘要：
我们介绍了各种着色原则，概括了所谓的“映射原则”的谢尔宾斯基更大的基数和一般理想。我们证明，这些原则捕获的概念，一个乌拉姆矩阵，并允许cumulative大基数，最显着的弱紧凑和不可言喻的红雀。我们还开发了这些着色原则的基本理论，将它们连接到经典的负方括号分割关系，证明抽水定理，并决定他们的各种情况。我们还表明，我们的原则提供了一个统一的方式来获得非饱和结果的理想满足一个属性，我们称之为次常态的上下文中，乌拉姆矩阵可能无法使用。
英文摘要：
We introduce various colouring principles which generalise the so-called "onto mapping principle" of Sierpinski to larger cardinals and general ideals. We prove that these principles capture the notion of an Ulam matrix and allow to characterise large cardinals, most notably weakly compact and ineffable cardinals. We also develop the basic theory of these colouring principles, connecting them to the classical negative square bracket partition relations, proving pumping-up theorems, and deciding various instances of theirs. We also demonstrate that our principles provide a uniform way of obtaining non-saturation results for ideals satisfying a property we call subnormality in contexts where Ulam matrices might not be available.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
