Appalachian Set Theory 2006–2012: Iterated forcing and the Continuum Hypothesis
Appalachian Set Theory 2006–2012: Iterated forcing and the Continuum Hypothesis
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阿巴拉契亚集合论 2006-2012：迭代强迫和连续统假设
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
D. Milovich
中科院分区：
文献类型：
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作者：
Todd Eisworth;J. Moore;D. Milovich
评论。下面的笔记反映了 2009 年 5 月 29 日和 5 月 30 日在菲尔兹研究所举行的为期两天的教程的内容。大部分内容已经在文献中存在了一段时间（主要是在 [10] 的原始版本中），但由于各种原因被证明难以阅读和消化。这些讲座中包含的唯一新材料涉及第 6 节和第 7 节中提出的融合方案的概念，甚至这更多地与风格有关，而不是与数学有关。我们对迭代定理的介绍如下 [4]。 k-可迭代性条件是 [4] 和 [5] 中出现的内容的自然外推，其中提出了 א0-可迭代性条件的迭代定理（削弱了 < ω1-properness）。完全适当性的表述取自[8]。然而，我们强调，这些定义和定理实际上是对[10]中提出的 Shelah 定理和定义的技术和/或风格修改。有兴趣进一步阅读研讨会主题的人应参考：[1]、[4]、[5]、[8]、[10] 和 [12]。我们要感谢 Ilijas Farah、Miguel Angel Mota、Paul Shafer 和匿名审稿人的仔细阅读并提出了一些改进建议。
Remark. The notes which follow reflect the content of a two day tutorial which took place at the Fields Institute on 5/29 and 5/30 in 2009. Most of the content has existed in the literature for some time (primarily in the original edition of [10]) but has proved difficult to read and digest for various reasons. The only new material contained in these lectures concerns the notion of a fusion scheme presented in Sections 6 and 7 and even this has more to do with style than with mathematics. Our presentation of the iteration theorems follows [4]. The k-iterability condition is a natural extrapolation of what appears in [4] and [5], where the iteration theorem for the א0-iterability condition is presented (with a weakening of < ω1-properness). The formulation of complete properness is taken from [8]. We stress, however, these definitions and theorems are really technical and/or stylistic modifications of the theorems and definitions of Shelah presented in [10]. Those interested in further reading on the topic of the workshop should consult: [1], [4], [5], [8], [10], and [12]. We would like to thank Ilijas Farah, Miguel Angel Mota, Paul Shafer, and the anonymous referee for their careful reading and suggesting a number of improvements.