Successors of Singular Cardinals
Successors of Singular Cardinals
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单一枢机主教的继任者
DOI：
10.1007/978-1-4020-5764-9_16
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Todd Eisworth
中科院分区：
文献类型：
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作者：
Todd Eisworth
单个枢机的后继机是一个特例——尽管它们是后继枢机，但它们仍然可以表现出与大型枢机相关的一些典型行为。在这一章中，我们详细地研究了奇异基数后继的组合。我们使用平稳反射作为我们进入主题的切入点，我们概述了Magidor的证明，即这样一个基数反射的所有平稳子集都是一致的。进一步考虑Magidor的证明，我们可以看到Shelah的理想i [λ]和相关的可接近性（AP）；我们对这些题目作了相当全面的论述。在此基础上，我们转向正方形、尺度，以及这些物体对有关反射现象的问题的影响。本章最后简要介绍了方括号划分关系及其与猜球原则的关系。
Successors of singular cardinals are a peculiar—although they are successor cardinals, they can still exhibit some of the behaviors typically associated with large cardinals. In this chapter, we examine the combinatorics of successors of singular cardinals in detail. We use stationary reflection as our point of entry into the subject, and we sketch Magidor’s proof that it is consistent that all stationary subsets of such a cardinal reflect. Further consideration of Magidor’s proof brings us to Shelah’s idealI[λ] and the related Approachability Property (AP); we give a fairly comprehensive treatment of these topics. Building on this, we then turn to squares, scales, and the influence these objects exert on questions of pertaining to reflection phenomena. The chapter concludes with a brief look at square-brackets partition relations and their relation to club-guessing principles.