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

组合技术主要由阿利斯泰尔 西蒙弗雷泽大学的Lachlan已经被证明是有效的 一些分类项目涉及同质 结构. 研究人员打算开发这套 在寻找新的结构类别中的进一步技术 不能以这种方式分析。 他会跟进的 麻省理工学院的Ehud Hrushovski的研究进展。通过尝试构建 新的强极小集与代数风味或证明 他们根本不存在 模型论中的另外两个问题 代数也在他的议程上。 这类模型论代数是 数理逻辑与古典代数学研究 结构. 它有自己独特的风味，但可以 揭示了传统的 这类结构的分类和分析方法。

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.