Mathematical Sciences: Homogeneous Structures, Strongly Minimal Sets, Model Theoretic Algebra

数学科学：齐次结构、强极小集、模型理论代数

• 批准号: 8903006
• 负责人: Gregory Cherlin
• 金额: $ 13.61万
• 依托单位: Rutgers University New Brunswick
• 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 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903006&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Homogeneous; Structures; Strongly

Combinatorial techniques developed primarily by Alistair Lachlan of Simon Fraser University have proved to be effective in a number of classification projects involving homogeneous structures. The investigator intends to develop this set of techniques further in the search for new classes of structures which cannot be analyzed in this fashion. He will follow up progress by Ehud Hrushovski of M.I.T. by attempting to construct new strongly minimal sets with an algebraic flavor or to prove that they do not exist. Two other problems in model theoretic algebra are also on his agenda. Model theoretic algebra of this sort is a mixture of mathematical logic and the study of classical algebraic structures. It has a characteristic flavor of its own but can shed light on difficuties which have arisen in traditional approaches to the classification and analysis of such structures.

西蒙·弗雷泽大学（Simon Fraser University）的Alistair Lachlan主要开发的组合技术已被证明在许多涉及同质结构的分类项目中有效。 研究人员打算在寻找无法以这种方式进行分析的新的结构中进一步开发这组技术。 他将跟进M.I.T.的Ehud Hrushovski的进度。通过试图用代数风味构建新的最小套装，或证明它们不存在。 模型理论代数中的另外两个问题也在他的议程中。 这种模型的理论代数是数学逻辑和经典代数结构的研究的混合物。 它具有自己的特征风味，但可以揭示出艰难的艰难，这些困难是在传统的分类和分析此类结构的方法中产生的。