Mathematical Sciences: Set Theory

数学科学：集合论

• 批准号: 8903380
• 负责人: Sy Friedman
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903380&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Set; Theory

S. D. Friedman's research is concerned mainly with definability problems in set theory, particularly applications of the so-called coding method invented by Ronald Jensen. Various problems and their relationship to the constructible universe of Godel and to certain other models of set theory will be considered. These models, the higher core models, will also be objects of the research themselves, both in terms of absoluteness and fine-structural properties. A postdoctoral researcher, Michael Chris Laskowski, and an advanced graduate student will be involved too. Elementary set theory is for most mathematicians simply a convenient language in which to express mathematical facts about collections of objects of various kinds. A highly developed axiomatic set theory exists, however, driven by the desire to make the foundations of mathematics absolutely secure and free from paradox of any kind. Research of this nature is in some sense mathematical hygiene, for paradoxes of the infinite abound, and mathematical intuition is not fully reliable as a protection from them.

S.D. Friedman 的研究主要关注集合论中的可定义性问题，特别是 Ronald Jensen 发明的所谓编码方法的应用。 将考虑各种问题及其与哥德尔的可构造宇宙和某些其他集合论模型的关系。 这些模型，即更高的核心模型，无论是在绝对性还是精细结构特性上，本身也将成为研究的对象。 博士后研究员迈克尔·克里斯·拉斯科夫斯基（Michael Chris Laskowski）和一名高级研究生也将参与其中。 对于大多数数学家来说，基本集合论只是一种方便的语言，用于表达有关各种对象集合的数学事实。 然而，存在一种高度发展的公理集合论，其驱动力是使数学基础绝对安全且不受任何形式的悖论的驱动。 这种性质的研究在某种意义上是数学卫生学，因为无限的悖论比比皆是，而数学直觉作为对它们的保护并不完全可靠。