不可数linear orders的五元素基础
A five element basis for the uncountable linear orders
摘要：
在本文中，我将表明，它是相对一致的，与通常的数学公理（ZFC）连同一个强形式的公理的无穷大（存在一个超紧基数），类的不可数线性秩序有一个五元素的基础。事实上，这样的一个基础来自于适当的强迫公理，一个强形式的贝尔范畴定理。元素是X，omega_1，omega_1^*，C，C^* 其中X是基数实aleph_1的任何子序，C是任何Countryman线。这证实了希拉的一个长期猜想。
英文摘要：
In this paper I will show that it is relatively consistent with the usual axioms of mathematics (ZFC) together with a strong form of the axiom of infinity (the existence of a supercompact cardinal) that the class of uncountable linear orders has a five element basis. In fact such a basis follows from the Proper Forcing Axiom, a strong form of the Baire Category Theorem. The elements are X, omega_1, omega_1^*, C, C^* where X is any suborder of the reals of cardinality aleph_1 and C is any Countryman line. This confirms a longstanding conjecture of Shelah.
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。
