Mathematical Sciences: Research in Model Theory

9308768鲍德温·鲍德温打算研究作为具有尺寸函数的有限结构类的齐次通用模型而得到的稳定结构。近年来，这些结构显著地拓宽了稳定结构的类别。特别是，他问这种结构是否可能满足沃特或拉克兰猜想，即这种结构的理论是否可以有有限多个或Aleph-one可数模型。他还将研究有限结构类的“通用”模型与斯宾塞在“随机”模型研究方面的最新进展之间的关系。在过去的二十年里，稳定性理论发展了一种技术手段，用于详细研究一大类数学结构。齐伯认为，事实上，所有涉及的结构都与古典结构联系得非常紧密。赫鲁晓夫斯基对这一猜想提供了一个反例。鲍德温改进了他的构造，找到了一种新的非笛卡尔投影平面。鲍德温还发现了这些结构与随机图理论之间的密切联系。鲍德温打算研究这类新的结构：看看它们是否提供了其他一些长期存在的猜想的反例，并进一步探索了与随机图的联系。***

9308768 Baldwin Baldwin intends to investigate stable structures derived as the homogeneous universal model for classes of finite structures with dimension functions. These structures have significantly broadened the class of stable structures in recent years. In particular, he asks whether structures of this sort can possibly satisfy the Vaught or Lachlan conjectures, i.e. whether the theory of such a structure can have finitely many or aleph-one countable models. He will also study the relation between `generic' models for classes of finite structures and recent advances in the study of `random' models by Spencer. During the last twenty years stability theory has developed a technical apparatus for detailed investigation of a large class of mathematical structures. Zil'ber suggested that in fact all the structures involved were tied very closely to classical structures. Hrushovski provided a counterexample to this conjecture. Baldwin refined his construction to find a new non-Desarguesian projective plane. Baldwin also discovered a close connection between these structures and the theory of random graphs. Baldwin intends to study this new class of structures: to see whether they provide counterexamples to some other long standing conjectures and to explore further the connection with random graphs. ***