Mathematical Sciences: Set Theory: Sets of Real Numbers and Infinite Games

数学科学：集合论：实数集和无限博弈

• 批准号: 9505375
• 负责人: Tomek Bartoszynski
• 金额: --
• 依托单位: Boise State University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505375&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Set; Theory; Sets

9505375 Bartoszynski Bartoszynski and Scheepers' research is in set theory. Some of their problems are well-known, while others have arisen from more recent work. One common theme for many of these problems lies in establishing a link between forcing and inductive constructions. Another underlying goal is to express various properties of sets in the language of infinite games. It is expected that notions from model theory, forcing theory, combinatorial set theory and game theory will play a significant role in this research. With its roots in the work of Cantor, Hausdorff, Godel and Cohen, their projected research will deal with the notions of the infinite and some subtle ways in which these notions manifest themselves in areas of modern mathematics. The questions they explore are specifically focused on that area of mathematics known as "foundations," with answers that potentially extend beyond its boundaries. In essence, their approach will apply the advanced methods of modern logic and game theory to problems that lie in the intersection of foundations and real analysis. ***

Bartoszynski和Scheepers的研究是在集合论。他们的一些问题是众所周知的，而另一些则是在最近的工作中出现的。许多这类问题的一个共同主题是在强迫构造和归纳构造之间建立联系。另一个潜在目标是用无限博弈的语言表达集合的各种属性。期望模型理论、强迫理论、组合集理论和博弈论的概念将在本研究中发挥重要作用。以康托尔、豪斯多夫、哥德尔和科恩的作品为基础，他们计划的研究将涉及无限的概念，以及这些概念在现代数学领域中表现出来的一些微妙方式。他们探索的问题特别集中在被称为“基础”的数学领域，其答案可能超出其边界。从本质上讲，他们的方法将应用现代逻辑和博弈论的先进方法来解决基础和实际分析交叉的问题。＊＊＊