Mathematical Sciences: Inevitability in Model Theory

数学科学：模型论的必然性

• 批准号: 9403701
• 负责人: Michael Chris Laskowski
• 金额: $ 6.09万
• 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: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9403701&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Inevitability; Model; Theory

9403701 Laskowski Dr. Michael Laskowski will continue his research in the field of model theory, a branch of mathematical logic. He expects to obtain more information as to the possible mechanisms making a type inevitable in the setting of superstable theories that do not have the Dimensional Order Property (DOP). Laskowski expects to complete his classification of those countable theories for which there are two non-isomorphic models that can be forced isomorphic by a forcing with the countable chain condition. Finally, he will continue his research into an inherent asymmetry between two new methods of constructing models of small, superstable theories. Most of the field of model theory (as a branch of mathematical logic) is concerned with developing methods for building algebraic structures with certain properties. The problem of whether there is a structure having an element satisfying an infinite set of properties (i.e., realizing a type) is well understood: such a structure exists if and only if, for every finite subset of the type, there is an element satisfying each of these properties. However, it is a much more subtle question to ask whether a given type is inevitable, i.e., whether EVERY structure contains an element realizing the type. Without adding additional restrictions to the class of structures under consideration, it is known that there can be no satisfactory criterion for which types are inevitable. Laskowski will continue his research on what additional constraints must be placed on the algebraic structure to yield a natural characterization of inevitability. ***

小行星9403701 Michael Laskowski博士将继续他在数学逻辑的一个分支模型理论领域的研究。 他希望获得更多的信息，以了解在不具有维序性质（DOP）的超稳定理论中，使一种类型不可避免的可能机制。 Laskowski期望完成他的分类那些可数理论，有两个非同构的模型，可以强迫同构的强迫与可数链条件。 最后，他将继续研究两种构建小型超稳定理论模型的新方法之间的内在不对称性。 模型论（作为数理逻辑的一个分支）的大部分领域都与建立具有某些性质的代数结构的方法有关。 是否存在具有满足无限性质集的元素的结构的问题（即，实现一个类型）是很好理解的：这样的结构存在当且仅当，对于该类型的每个有限子集，有一个元素满足这些属性中的每一个。 然而，这是一个更微妙的问题，问一个给定的类型是否是不可避免的，即，是否每个结构都包含实现该类型的元素。 如果不对所考虑的结构类别增加额外的限制，我们知道，对于哪些类型是不可避免的，不可能有令人满意的标准。 Laskowski将继续他的研究什么额外的限制必须放在代数结构产生自然表征的必然性。 ***