Forcing, Combinatorics and Definability
Forcing, Combinatorics and Definability
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强迫、组合学和可定义性
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发表时间：
2010
期刊：
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通讯作者：
S. Friedman
中科院分区：
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作者：
S. Friedman
在这些讲座中，我将重点讨论集合论中的强迫、组合方法和可定义性问题之间的相互作用。这些主题之间的相互作用非常富有成效，我将在以下三个上下文中对其进行说明：可定义的 Wellorders、不可数 Cardrnals 的基本特征和 $Prcdot oper$ 的模型。强制 $ng$ 公理。第一个主题是集合论中的经典主题，尽管最近已经证明了有趣的结果并且仍然存在有趣的开放问题。第二个主题相当新，为新强迫方法的应用提供了肥沃的土壤。最后一个主题更加专业，但确实带来了一些惊喜，并导致了一种新的强制迭代。
In these lectures I will focus on the interaction between forcing, combinatorial methods and definability issues in set theory. The interplay between these topics has been remarkably fruitful, and I will illustrate it in the following three contexts: Definable Wellorders, Cardinal Characteristics at Uncountable Cardrnals and Models of the $Prcdot oper$ . Forct $ng$ Axiom. The first of these topics is a classical one in set theory, although interesting results have recently been proved and interesting open problems remain. The second of these topics is quite new and provides fertile ground for the application of new forcing methods. The last topic is more specialised but does hold some surprises and has led to a new kind of forcing iteration.