Research in Model Theory

鲍德温在模型理论中提出了三个主题：抽象初等类、域的类属扩展和通过命名谓词在扩展下保持稳定性。最后两个主题在某种意义上是对偶的。二十岁的Searchfor a Bad-field试图构造一个复数的足够通用的子群，以保持omega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，Baldwin正在和Baizhanov一起探索，当一个子集被命名时，在最一般的条件下可以希望保持稳定性。鲍德温一直在写一本专著，总结抽象初级课程的莫利定理的现状。这本专著试图澄清和组织这一主题的一般工作，强调与Zilber关于复杂几何的工作和`Hrushovskucture‘之间的联系，并为本文中更广泛的稳定性理论奠定基础。在鲍德温的工作中，从理解各种数学主题的基础的一般逻辑角度提供了从数据库理论(计算机科学)、随机图、抽象代数和复数分析等不同领域的联系。在许多情况下，逻辑的作用是对可以证明的东西进行限制，并将研究引向更有成效的努力。在过去的15年里，鲍德温一直是逻辑界和数学教育界的纽带。他目前是UIC数学教育办公室的主任。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。一个对学校数学有深刻理解的教师不仅知道中学数学的概念结构，而且还了解学生解决问题的常见策略和常见的学生误解。逻辑学背景在帮助未来的教师培养清晰地交流数学的能力方面是无价的。

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.