NSF-BSF Combinatorial Set Theory and PCF

NSF-BSF 组合集合论和 PCF

• 批准号: 2400200
• 负责人: Erick Eisworth
• 金额: $ 18.48万
• 依托单位: Ohio University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-07-01 至 2027-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2400200&HistoricalAwards=false
• 关键词: NSF; BSF; Combinatorial; Set; Theory

This project supports advanced mathematical research and training in an underserved area of the United States (Appalachia) by leveraging funding from the NSF-BSF program to build an international partnership between the PI and a colleague at Ben-Gurion University in Israel. We will develop a horizontal collaborative structure bridging the two institutions to allow us to combine our expertise. Using a pedagogical model we pioneered during the pandemic, we will involve students in both countries in collaborative research centered on the mathematical research of the senior personnel in the grant.The research component of the project is centered on PCF(Possible CoFinality) theory, a body of work developed by Shelah to analyze cardinal arithmetic in set theory. Shelah obtained fantastic results in set theory and other fields by using these techniques, but even after three decades, the full implications of PCF theory at singular fixed points are not fully understood. Our project addresses this gap by continuing the recent work of the PI and his Israeli counterpart, with a focus on mapping out the extent to which PCF theory imposes constraints in cardinal arithmetic and infinitary Ramsey theory.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目利用 NSF-BSF 计划的资金，在 PI 和以色列本古里安大学的同事之间建立国际合作伙伴关系，支持美国服务欠缺地区（阿巴拉契亚）的高级数学研究和培训。 我们将建立一个连接两个机构的横向合作结构，使我们能够结合我们的专业知识。 利用我们在疫情期间首创的教学模式，我们将让两国学生参与以高级人员的数学研究为中心的合作研究。该项目的研究部分以PCF（Possible CoFinality）理论为中心， Shelah 开发的用于分析集合论中基数算术的工作主体。 Shelah 通过使用这些技术在集合论和其他领域取得了出色的成果，但即使在三十年后，PCF 理论在奇异不动点上的全部含义仍未完全理解。 我们的项目通过继续 PI 及其以色列同行最近的工作来解决这一差距，重点是确定 PCF 理论对基数算术和无限拉姆齐理论施加约束的程度。该奖项反映了 NSF 的法定使命，并被视为值得通过使用基金会的智力优点和更广泛的影响审查标准进行评估来支持。