Mathematical Sciences: Set Theory and Analysis

卡尔森将致力于以下四个问题和相关的 问题： (1)这些强贫乏集构成理想集吗？ (2)沿着内部模型层次结构中， 覆盖引理hold？ (3)关于多同构模型的Fraisse猜想 子结构始终是假的？ (4)中间极限的存在性能在集合中证明吗 理论？ 这些都是技术问题， 公理集合论 人们想知道在什么假设下 它们是真的，是否存在集合论的模型， 他们失败了，其他人也失败了。 这是微妙的问题 比如这些让我们能够探索 所有数学在逻辑上所依赖的公理系统。

Carlson will work on the following four problems and related issues: (1) Do the strongly meager sets form an ideal? (2) How far along the inner model hierarchy do strong covering lemmas hold? (3) Is Fraisse's conjecture on models with many isomorphic substructures consistently false? (4) Can the existence of medial limits be proved in set theory? These are technical questions lying at the foundations of axiomatic set theory. One wants to know under what assumptions they are true, whether there are models of set theory in which they fail and others in which they hold. It is subtle questions such as these that allow us to explore the limits of the axiomatic systems upon which all of mathematics logically rests.