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.

该项目通过利用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，支持美国服务不足地区（阿巴拉契亚）的高级数学研究和培训。 我们将建立一个横向合作结构，将两个机构联系起来，使我们能够联合收割机结合我们的专门知识。 利用我们在疫情期间开创的教学模式，我们将让两国学生参与以赠款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（可能共终结性）理论为中心，这是Shelah开发的一系列工作，用于分析集合论中的基数算术。Shelah使用这些技术在集合论和其他领域获得了惊人的结果，但即使在三十年后，PCF理论在奇异不动点上的全部含义仍然没有完全理解。 我们的项目通过继续PI和他的以色列同行最近的工作来解决这个差距，重点是绘制出PCF理论在基数算术和无穷拉姆齐理论中施加约束的程度。这个奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。