Mathematical Sciences: Set Theory

数学科学：集合论

• 批准号: 9322442
• 负责人: William Woodin
• 金额: $ 27.5万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9322442&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Set; Theory

9322442 Woodin The focus of the project is the relationship between large cardinal axioms and determinacy axioms. This is interpreted somewhat broadly and is meant to include, for example, the study of a new class of models. These models are generated as forcing extensions of models in which the axiom of determinacy holds. They are interesting because they provide the first examples of canonical models in which the Continuum Hypothesis is false. One consequence of Kurt Godel's results of 60 years ago is that there will always be mathematical problems which cannot be solved. This first became a practical concern 30 years ago when Paul Cohen showed that Cantor's Continuum Hypothesis cannot be settled. Since Cohen's work, numerous problems have been shown to be unsolvable. The large cardinal hierarchy provides in many cases a resolution to the problem of independence. This is done, not by resolving the question, but rather by calibrating the degree to which it is unsolvable. This hierarchy of axioms, each of which asserts the existence of a new infinity, emerges as the fundamental mathematical reality. The investigator intends to study this hierarchy in its many manifestations. ***

9322442伍德丁项目的重点是大型基本公理与确定性公理之间的关系。 这是广泛的解释，旨在包括例如对新模型的研究。 这些模型的生成是迫使确定性公理所拥有的模型的扩展。 它们很有趣，因为它们提供了连续假设是错误的规范模型的第一个例子。 库尔特·戈德尔（Kurt Godel）60年前的结果的结果之一是，总会有数学问题无法解决。 当保罗·科恩（Paul Cohen）表明康托尔（Cantor）的连续假设无法解决时，这首先成为了实际问题。 自科恩（Cohen）的工作以来，已经证明许多问题是无法解决的。 大型的基本层次结构在许多情况下为独立问题提供了解决方案。 这不是通过解决问题而是通过校准无法解决的程度来完成的。 公理的这种层次结构，每个公理的存在，都认为新的无穷大的存在是基本的数学现实。 研究人员打算在其许多表现形式中研究这种层次结构。 ***