Mathematical Sciences: Descriptive Locale Theory

数学科学：描述性场所理论

• 批准号: 9003834
• 负责人: John Isbell
• 金额: $ 2万
• 依托单位: SUNY at Buffalo
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-15 至 1991-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003834&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Descriptive; Locale; Theory

Isbell will continue his study of a reinterpretation of descriptive set theory, the natural interpretation in metrizable locales. This shift has already been shown to produce at least one gain in metrizable spaces (the standard setting) although there are three or four losses. The completed work is almost all in Borel multiplicative class 1. Most of the main problems now visible are in multiplicative class 2 (F-sigma-delta). Hopeful indications that the technical losses by the central reinterpretation may be outweighed by conceptual enrichment are to be explored. The goal is to shed light on standard descriptive set theory by demonstrating the existence of an alternative.

伊斯贝尔将继续他对描述集合论的重新解释的研究，描述集合论是可度量区域中的自然解释。这种转变已经被证明在可计量空间(标准设置)中至少产生了一次收益，尽管存在三到四次损失。已完成的工作几乎都是在Borel乘法类1中完成的。目前可见的主要问题大多在乘法类2(F-sigma-Delta)中。将探索有希望的迹象表明，中央重新解释造成的技术损失可能会被概念丰富所抵消。其目的是通过证明替代方案的存在来阐明标准描述性集合论。