Applications of Set Theory to Analysis

集合论在分析中的应用

• 批准号: 8553-2012
• 负责人: Steprans, Juris
• 金额: $ 1.82万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568602
• 关键词: Applications; Set; Theory; Analysis

It has been know since the work of Kurt Godel in the 1930s that there are statements in mathematics that can neither be proved nor disproved; but these statements were quite artificial and it could be argued that they would never arise in any natural context. However, in the early 1960s Paul Cohen showed that there are statements that can not be decided about which mathematicians actually care and which arise naturally in their subject. The technique he developed for doing this has since found many applications and the undecidable statements now come from areas where one would not have guessed undecidability could be found. This proposal continues the program of looking for statements in mathematics, analysis to be precise, where such phenomena occur. The significance of this project to Canadian science is that it provides a vehicle for training the next generation of Canada's research mathematicians. In order for Canada to benefit from global advances in science, mathematics in particular, it must support a body of researchers who are acknowledged internationally to be contributing to the global research enterprise in a significant way. This research project will allow talented students and postdoctoral fellows to establish reputations that will allow them to participate in international, cutting edge research projects from which Canadian science can benefit.

自从1930年代库尔特·戈德尔（Kurt Godel）的工作以来，就已经知道数学上的陈述既不能被证明也不能被证明。但是这些陈述是非常人为的，可以说它们在任何自然背景下永远不会出现。但是，在1960年代初期，保罗·科恩（Paul Cohen）表明，有些陈述无法决定哪个数学家实际在乎，并且在他们的主题中自然出现。此后，他为此开发的技术发现了许多应用程序，而不可确定的陈述现在来自人们无法猜测不可证明的领域。该建议继续寻找数学中的陈述的计划，确切的分析以及发生这种现象的地方。 该项目对加拿大科学的重要性是，它为培训加拿大下一代研究数学家提供了一种工具。为了使加拿大从科学方面的全球进步中受益，尤其是数学，它必须支持一群在国际上承认的研究人员，以重大的方式为全球研究企业做出贡献。该研究项目将使才华横溢的学生和博士后研究员能够建立声誉，使他们能够参加加拿大科学可以从中受益的国际尖端研究项目。