Mathematical Sciences: Research in Model Theory

首席研究员将继续研究模型 模型论：一种福尔斯属于模型论的两个总标题的理论 有序结构和一元二阶逻辑。 在几年前开始的研究中，他研究了 O-最小结构。 这项工作统一了模型 几类特殊线性序的理论 结构，并产生了一般性的结果，以前只知道在 特殊情况。 他希望考虑几个问题 关于O-最小结构 最重要的是，他计划 试图发展一个类似的稳定性理论的线性 有序的结构，并调查的可能性， 结构类的一般模型理论 拓扑以一阶方式给出。 主要研究者目前还从事 与Y. 古列维奇关于一元二阶 “数学逻辑的观点”系列。 这 这本书将调查丰富多样的方法， 用于证明的可判定性或不可判定性的 一元二阶理论的各种结构，也是 使用这些方法获得的结果。 这本书 将被写入，以便感兴趣的两个逻辑学家和 理论计算机科学家

The principal investigator will continue research in model theory that falls under the two general headings of model theory for ordered structures and monadic second-order logic. In research begun several years ago, he studied the notion of an o-minimal structure. This work has unified the model theory for several specific classes of linearly ordered structures, and has yielded general results known before only in special cases. He wishes to consider several questions concerning o-minimal structures. Most importantly, he plans to attempt to develop an analogue to stability theory for linearly ordered structures, and to investigate the possibilities for a general model theory for classes of structures whose natural topology is given in a first-order way. The principal investigator also is currently engaged in writing a monograph with Y. Gurevich on monadic second-order logic for the "Perspectives in Mathematical Logic" series. This book will survey both the rich variety of methods that have been employed to prove the decidability or undecidability of the monadic second-order theory of various structures, and also the results that have been obtained using these methods. The book will be written so as to be of interest to both logicians and theoretical computer scientists.