论文标题
大型红衣主教的景观
The Landscape of Large Cardinals
论文作者
论文摘要
本文的目的是提供集合理论中大型基础层次结构的介绍性概述。在大型的红衣主教中，我们的意思是任何基本$κ$，其存在足以证明ZFC的一致性。我们假定对集合理论，模型理论和ZFC公理的基本熟悉，尽管将根据需要进行审查。我们试图阐明较高无限的广阔景观，激发了一些已知的大型红衣主教的定义（但肯定不是全部）。我们还讨论了与连续假设的联系，并就大型红衣主教一致性的信念提供了一些哲学思考。
The purpose of this paper is to provide an introductory overview of the large cardinal hierarchy in set theory. By a large cardinal, we mean any cardinal $κ$ whose existence is strong enough of an assumption to prove the consistency of ZFC. We assume basic familiarity with set theory, model theory, and the ZFC axioms, though certain concepts will be reviewed as necessary. We attempt to clarify the vast landscape of the higher infinite, motivating the definitions of some (but certainly not all) of the known large cardinals. We also discuss connections with the Continuum Hypothesis and provide some philosophical reflections on belief in the consistency of large cardinals.
