Research in Model Theory: Generic Structures

模型理论研究：泛型结构

• 批准号: 0203747
• 负责人: Kitty Holland
• 金额: --
• 依托单位: Northern Illinois University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-06-15 至 2007-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0203747&HistoricalAwards=false
• 关键词: Research; Model; Theory; Generic; Structures

AbstractAward: DMS-0203747Principal Investigator: Kitty L. HollandHolland's proposed work centers on applying the Hrushovski-styleamalgamation technique to produce novel examples of omega-stablestructures. Together with Baldwin, Holland is engaged in anattempt to use this technique to produce a bad field. Holland'swork toward this end has produced algebro-geometric results ofindependent interest on the relationship between transcendencedegree and multiplicative group rank in characteristic zerofields. Holland proposes to exploit this work to complete thebad field project with Baldwin and to extend thealgebro-geometric results. She further proposes to settlestability questions for certain structures produced by thetechnique; to analyze the geometries of structures produced bythe technique and to extend her joint work with Baldwin toward anabstract model theoretic analysis of the technique and itsproducts.Since its introduction in the early 90s, Hrushovski'samalgamation technique has been applied with great success tosettle a variety of old existence conjectures central toalgebraic model theory. Holland's ambition, embodied in thisproposal, is threefold: To continue breaking new ground inapplication of the technique, to explore the limitations of thetechnique by characterizing common properties of its products,and to make the technique more widely and efficiently applicableby extracting common difficulties arising in its implementationand dealing with them uniformly on an abstract level.Holland's proposed work centers on applying the Hrushovski-styleamalgamation technique to produce novel examples of omega-stablestructures. Together with Baldwin, Holland is engaged in anattempt to use this technique to produce a bad field. Holland'swork toward this end has produced algebro-geometric results ofindependent interest on the relationship between transcendencedegree and multiplicative group rank in characteristic zerofields. Holland proposes to exploit this work to complete thebad field project with Baldwin and to extend thealgebro-geometric results. She further proposes to settlestability questions for certain structures produced by thetechnique; to analyze the geometries of structures produced bythe technique and to extend her joint work with Baldwin toward anabstract model theoretic analysis of the technique and itsproducts.Since its introduction in the early 90s, Hrushovski'samalgamation technique has been applied with great success tosettle a variety of old existence conjectures central toalgebraic model theory. Holland's ambition, embodied in thisproposal, is threefold: To continue breaking new ground inapplication of the technique, to explore the limitations of thetechnique by characterizing common properties of its products,and to make the technique more widely and efficiently applicableby extracting common difficulties arising in its implementationand dealing with them uniformly on an abstract level.

摘要奖：DMS-0203747首席研究员：Kitty L.HollandHolland建议的工作重点是应用Hrushovski风格的融合技术来产生欧米茄稳定结构的新例子。与鲍德温一起，霍兰德正在尝试使用这种技术来制造一个糟糕的磁场。Holland为此目的所做的工作已经产生了依赖于特征零域中超越度与乘法群秩间关系的代数几何结果。Holland建议利用这项工作与Baldwin一起完成糟糕的场项目，并推广代数几何结果。她还建议解决由该技术产生的某些结构的稳定性问题；分析由该技术产生的结构的几何形状，并将她与鲍德温的合作扩展到对该技术及其产品的抽象模型理论分析。自90年代初引入以来，Hrushovski的混合技术已成功地应用于各种古老的存在猜想的中心代数模型理论。霍兰德的雄心体现在这项建议中有三个方面：继续在该技术的应用上取得新的突破，通过表征其产品的共同特性来探索该技术的局限性，通过提取在实施中出现的共同困难并在抽象层面上统一处理来使该技术更广泛和更有效地应用。霍兰德提议的工作重点是应用赫鲁晓夫斯基式的融合技术来产生欧米伽稳定结构的新例子。与鲍德温一起，霍兰德正在尝试使用这种技术来制造一个糟糕的磁场。Holland为此目的所做的工作已经产生了依赖于特征零域中超越度与乘法群秩间关系的代数几何结果。Holland建议利用这项工作与Baldwin一起完成糟糕的场项目，并推广代数几何结果。她还建议解决由该技术产生的某些结构的稳定性问题；分析由该技术产生的结构的几何形状，并将她与鲍德温的合作扩展到对该技术及其产品的抽象模型理论分析。自90年代初引入以来，Hrushovski的混合技术已成功地应用于各种古老的存在猜想的中心代数模型理论。荷兰的雄心体现在这项提议中有三个方面：继续在技术应用方面开辟新的道路，通过描述其产品的共同特性来探索技术的局限性，以及通过提取在实施中出现的共同困难并在抽象层面上统一处理来使技术得到更广泛和有效的应用。