Structure Theorems in Model Theory

模型论中的结构定理

• 批准号: 0901336
• 负责人: Michael Chris Laskowski
• 金额: $ 30.81万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-06-01 至 2013-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901336&HistoricalAwards=false
• 关键词: Structure; Theorems; Model; Theory

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).Laskowski is continuing his research in model theory, which is a branch of mathematical logic. The bulk of his research is organized around the theme of obtaining better structure theorems in three distinct settings. He will continue his investigations of the fine structure of models of classifiable theories with an eye on extensions to uncountable languages, look for a generalization of Shelah's notion of excellence that is applicable to more classes of structures, and seek more instances where stability theoretic assumptions automatically bound the quantifier complexity of the formulas. Additionally, Laskowski will attempt to answer specific questions about dependent formulas, elementary extensions of expansions of Archimedean ordered abelian groups, the Schroeder-Bernstein property of a theory, and a long standing decidability question from symbolic dynamics.Model theory is concerned with the interplay between theories, i.e., sets of sentences in a very formal language, and the classes of algebraic structures (models) that satisfy these sentences. There is a well established taxonomy of theories, which is based on the embeddability or non-embeddability of certain configurations of elements into models of the theory. Laskowski has identified certain classes of theories that have direct connections to limitations on data compression and computational learning theory, and will continue his examination of these theories.

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。Laskowski正在继续他在模型理论方面的研究，这是数理逻辑的一个分支。他的大部分研究是围绕在三个不同的设置获得更好的结构定理的主题组织的。他将继续他的调查的精细结构模型的可分类的理论着眼于扩展到不可数的语言，寻找一个概括的谢拉的概念，卓越的是适用于更多类别的结构，并寻求更多的情况下，稳定性理论的假设自动约束的量词复杂性的公式。此外，Laskowski将试图回答有关相关公式的具体问题，阿基米德有序阿贝尔群的扩展的基本扩展，理论的Schroeder-Bernstein属性，以及符号动力学的长期可判定性问题。模型理论关注理论之间的相互作用，即，一种非常正式的语言中的句子集合，以及满足这些句子的代数结构（模型）的类。 理论有一个很好的分类，它基于某些元素配置到理论模型中的嵌入性或非嵌入性。Laskowski已经确定了某些类别的理论，这些理论与数据压缩和计算学习理论的局限性有直接联系，并将继续对这些理论进行研究。