Research in Model Theory

Baldwin在模型论中提出了三个主题的工作：抽象的基本类，域的类属扩展，以及通过命名谓词在扩展下保持稳定性。 二十年前的坏域研究试图构造一个足够通用的复数子群，以保持Ω稳定性。 模型理论和代数工具都是必不可少的。 在另一个方向鲍德温正在探索与Baizhanov，最一般的条件下，可以希望保持稳定时，一个子集的名称。 鲍德温一直在写一本专著，总结抽象初等类的“莫利定理”的现状。 这本专著，试图澄清和组织的一般工作，在这个主题，强调与两个Zilber的工作，复杂的几何和`Hrushovskiconstruction的联系，并奠定了基础，为更一般的稳定性理论在这方面的工作。逻辑的一般观点，在理解的基础，各种数学主题提供了鲍德温的工作之间的联系，如数据库理论的不同领域（计算机科学），随机图，抽象代数和复分析。在许多情况下，逻辑的作用是对可以证明的内容进行限制，并将研究引导到更有成效的努力中。 在过去的15年里，鲍德温一直是逻辑和数学教育界的纽带。 他目前是UIC数学教育办公室主任。 他的目标是为未来的教师提供对基础中学数学的深刻理解。一个对中学数学有着深刻理解的教师，不仅要了解中学数学的概念结构，而且要了解学生解决问题的常见策略，以及学生常见的错误概念沿着。 逻辑学背景在帮助未来的教师发展清晰地交流数学的能力方面是非常宝贵的。

Baldwin proposes work on three topics in model theory: abstractelementary classes, generic expansions of fields, and thepreservation of stability under expansion by naming predicates.The last two are in some sense dual. The twenty year old searchfor a bad-field tries to construct a sufficiently generic subgroupof the complex numbers that omega stability is preserved. Bothrefined model theoretic and algebraic tools are essential. In theother direction Baldwin is exploring with Baizhanov, the mostgeneral conditions under which can hope to preserve stability whena subset is named. Baldwin has been writing a monographsummarizing the current state of `Morley's theorem' for AbstractElementary Classes. This monograph, tries to clarify and organizethe general work in this topic, underline the connections withboth Zilber's work on complex geometry and the `Hrushovskiconstruction, and lay the foundation for a more general stabilitytheory in this context.The general perspective of logic in understanding the foundationsof various mathematical topics has provided in Baldwin's worklinks among fields as diverse as database theory (computerscience), random graphs, abstract algebra and complex analysis. Inmany cases the role of logic is place limits on what can be provedand direct research into more productive endeavors. Baldwin hasserved as a link between the logic and mathematics educationcommunities for the last fifteen years. He is currently directorof the Office of Mathematics Education at UIC. He aims to providefuture teachers with a profound understanding of fundamentalsecondary school mathematics. A teacher with profoundunderstanding of school mathematics is not only aware of theconceptual structure of secondary mathematics, but alsounderstands the common strategies that students use to solveproblems along with common student misconceptions. A backgroundin logic is invaluable in helping future teachers develop theability to communicate mathematics clearly.