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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=592932
• 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 20 世纪 30 年代库尔特·哥德尔 (Kurt Godel) 的工作以来，人们就知道数学中有些陈述既不能被证明，也不能被反驳。但这些陈述相当人为，可以说它们永远不会在任何自然环境中出现。然而，在 20 世纪 60 年代初，保罗·科恩 (Paul Cohen) 表明，对于哪些数学家真正关心哪些数学家真正关心哪些数学家以及哪些数学家在他们的学科中自然出现的数学问题无法确定。他为此开发的技术已经找到了许多应用程序，并且不可判定的语句现在来自人们不会猜测会发现不可判定性的领域。该提案延续了在数学中寻找陈述的计划，准确地说是分析，在这种现象发生的地方。