Mathematical Sciences: Set Theory

弗里德曼的研究主要涉及集合论中的可定义性问题，特别是罗纳德·詹森发明的所谓编码方法的应用。各种问题及其与哥德尔的可构造宇宙和集合论的某些其他模型的关系将被考虑。这些模型，即更高的核心模型，也将是研究本身的对象，无论是在绝对性方面还是在精细结构性质方面。博士后研究员迈克尔·克里斯·拉斯科夫斯基和一名高级研究生也将参与其中。对于大多数数学家来说，初等集合论只是一种方便的语言，用来表达关于各种对象集合的数学事实。然而，一个高度发达的公理集合论的存在，是由使数学基础绝对安全和不存在任何类型的悖论的愿望推动的。这种性质的研究在某种意义上是数学上的卫生，因为无限的悖论比比皆是，而数学直觉并不完全可靠地保护人们免受它们的侵害。

S. D. Friedman's research is concerned mainly with definability problems in set theory, particularly applications of the so-called coding method invented by Ronald Jensen. Various problems and their relationship to the constructible universe of Godel and to certain other models of set theory will be considered. These models, the higher core models, will also be objects of the research themselves, both in terms of absoluteness and fine-structural properties. A postdoctoral researcher, Michael Chris Laskowski, and an advanced graduate student will be involved too. Elementary set theory is for most mathematicians simply a convenient language in which to express mathematical facts about collections of objects of various kinds. A highly developed axiomatic set theory exists, however, driven by the desire to make the foundations of mathematics absolutely secure and free from paradox of any kind. Research of this nature is in some sense mathematical hygiene, for paradoxes of the infinite abound, and mathematical intuition is not fully reliable as a protection from them.