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: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508781
• 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.

自从库尔特·哥德尔在20世纪30年代的工作以来，人们就知道数学中有一些陈述既不能被证明也不能被证伪;但是这些陈述是相当人为的，可以说它们永远不会出现在任何自然环境中。然而，在20世纪60年代初，保罗·科恩（Paul Cohen）指出，有些陈述无法确定哪些数学家真正关心，哪些陈述在他们的学科中自然出现。他开发的技术，这样做，因为发现了许多应用程序和不可判定的语句现在来自的领域，人们不会猜到不可判定性可以发现。这一建议继续程序寻找语句在数学，分析是准确的，在这种现象发生。