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

主要由西蒙·弗雷泽大学的阿利斯泰尔·拉克伦开发的组合技术已被证明在一些涉及同质结构的分类项目中是有效的。研究人员打算进一步发展这套技术，以寻找不能以这种方式分析的新的结构类别。他将跟进麻省理工学院的Ehud Hrushovski的进展，试图构造具有代数味道的新的强极小集，或者证明它们不存在。模型论代数中的另外两个问题也在他的议程上。这类模型理论代数是数理逻辑和经典代数结构研究的混合体。它有其自身的特点，但可以揭示在对这类结构进行分类和分析的传统方法中出现的困难。

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.