Research in Model Theory: Generic Structures

摘要奖：DMS-0203747主要研究者：Kitty L. Holland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产生一个糟糕的领域。 Holland的工作已经产生了关于超越度和乘法群秩在特征零域中的关系的代数几何结果。 Holland建议利用这一工作来完成Baldwin的bad field项目并推广代数几何结果。 她进一步提出解决稳定性问题的某些结构所产生的技术，分析几何结构所产生的技术，并延长她的联合工作鲍德温对抽象的模型理论分析的技术及其产品。自90年代初推出以来，Hrushovski 'samalgamation技术已被成功地应用于解决各种旧的存在问题中央代数模型理论。 荷兰的雄心，体现在这个建议中，有三个方面：继续在该技术的应用中开辟新天地，通过表征其产品的共同特性来探索该技术的局限性，并通过提取其实现中出现的常见困难并在抽象层面上统一处理这些困难，使该技术更广泛和有效地适用。styleamalgamation技术，以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产生一个糟糕的领域。 Holland的工作已经产生了关于超越度和乘法群秩在特征零域中的关系的代数几何结果。 Holland建议利用这一工作来完成Baldwin的bad field项目并推广代数几何结果。 她进一步提出解决稳定性问题的某些结构所产生的技术，分析几何结构所产生的技术，并延长她的联合工作鲍德温对抽象的模型理论分析的技术及其产品。自90年代初推出以来，Hrushovski 'samalgamation技术已被成功地应用于解决各种旧的存在问题中央代数模型理论。 霍兰德的野心，体现在这一建议，是三方面的：继续突破新领域的技术应用，探索技术的局限性，其产品的特点共同属性，并使技术更广泛和有效地适用，通过提取共同的困难，在其实施和处理他们统一在抽象的水平。

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.