New directions in the model theory of fields: an LMS Durham research symposium

场模型理论的新方向：LMS Durham 研究研讨会

• 批准号: EP/F068751/1
• 负责人: John Bolton
• 金额: $ 10.59万
• 依托单位: Durham University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2009
• 资助国家: 英国
• 起止时间: 2009 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FF068751%2F1
• 关键词: New; directions; model; theory; fields

Model theory is a branch of mathematical logic dealing with mathematical structures (models) from the point of view of first-order logical definability. Traditionally the subject has been subdivided into two, highly overlapping, areas: pure model theory and applied model theory. The latter is characterized by its applications to, and influences from, algebra, geometry and analysis.We propose to hold a 10-day conference in July 2009 at Durham University, organised by D. Macpherson (Leeds), A. Pillay (Leeds), M. Prest (Manchester) and A. Wilkie (Manchester). This will concentrate on applied model theory and its applications to certain specific areas of mainstream mathematics. We will invite many mainstream mathematicians from around the world who have taken on board, or expressed an interest in familiarizing themselves with, model theoretic methods. After the meeting, the model theorists will have a better understanding of those problems in the areas of mainstream mathematics covered in the symposium that are amenable to their methods, and therefore be in a better position to solve them. Also, the mathematicians present will become more aware of the scope of model theoretic methods within their own disciplines. The conference will focus on themes which show particular promise, and where interactions between different groups are likely to be of most benefit. There will be an uncluttered lecture programme, with ample opportunities for discussions, collaborations and informal talks. Our aim is to ensure that all are aware of the techniques and challenges that are arising for our areas of focus. To help achieve this we will have a short series of lectures on each of the three themes. Each series will have two lectures from a model theorist and two from a non-model theorist. By bringing together a broad range of experts, this meeting will have a significant impact on the development of these rich areas of research. The results of the meeting will be distributed initially via an actively-managed and easily accessible website, which will contain a list of participants, abstracts of talks and other relevant information. The main talks will be recorded (with permission of the speakers) via a web-cam, and be made freely available on the website within one month of the finish of the meeting. Lecture notes and/or slides will also be put on the site. A more detailed record of the meeting will be provided by the publication in research journals of cutting-edge articles inspired by the subjects covered in the meeting. The conference is expected to provide a major lasting fillip to world research in the model theory of fields and related areas.

模型论是数理逻辑的一个分支，从一阶逻辑可定义性的角度研究数学结构（模型）。传统上，这门学科被细分为两个高度重叠的领域：纯模型论和应用模型论。我们建议在2009年7月在达勒姆大学举办一个为期10天的会议，由D。Macpherson（利兹），A. Pillay（利兹），M. Prest（Manchester）和A.威尔基（曼彻斯特）。这将集中在应用模型理论及其应用到某些特定领域的主流数学。我们将邀请来自世界各地的许多主流数学家，他们已经采取了，或表示有兴趣熟悉模型理论方法。会议结束后，模型理论家将有一个更好的理解那些问题的主流数学领域涵盖的专题讨论会，是服从他们的方法，因此在一个更好的位置来解决这些问题。此外，在场的数学家将更加意识到模型理论方法在他们自己学科中的范围。会议将集中讨论那些特别有希望的主题，以及不同群体之间的互动可能最有益的主题。将有一个整洁的讲座计划，有充足的讨论、合作和非正式会谈的机会。我们的目标是确保所有人都意识到我们关注的领域正在出现的技术和挑战。为了帮助实现这一点，我们将有一个简短的系列讲座，对每一个三个主题。每个系列将有两个讲座从模型理论家和两个从非模型理论家。通过汇集广泛的专家，这次会议将对这些丰富的研究领域的发展产生重大影响。会议的结果将首先通过一个积极管理和容易进入的网站分发，该网站将载有与会者名单、会谈摘要和其他有关信息。主要演讲将通过网络摄像头进行录制（经演讲者许可），并在会议结束后一个月内在网站上免费提供。课堂讲稿和/或幻灯片也将放在网站上。会议的更详细记录将通过在研究期刊上发表受会议所涉主题启发的前沿文章来提供。这次会议有望为世界范围内的场模型理论及相关领域的研究提供一个重大而持久的推动力。

项目成果

Vapnik-Chervonenkis density in some theories without the independence property, I

在一些不具有独立性的理论中，Vapnik-Chervonenkis 密度，I

• DOI: 10.1090/tran/6659
• 发表时间: 2015
• 期刊: Transactions of the American Mathematical Society
• 影响因子: 1.3
• 作者: Aschenbrenner M