Mathematical Sciences: Combinatorial Set Theory, Forcing andPriority Arguments

鲍姆加特纳将致力于强迫理论和组合集合论中的问题，特别是似乎提出了关于强迫的基本问题的组合问题。强迫是检验集合论给定公理所允许的集合论行为的极端的一种强有力的方法。人们用它来构建符合公理的集合论模型，目的是证明一些额外的性质并不遵循公理。如果一个人能证明一个性质或它的对立面都不是从公理中推导出来的，那么他就找到了那个性质的独立性证明。它们被高度珍视，因为它们阐明了集合论的基础，从而照亮了所有数学的基础。

Baumgartner will work on problems in the theory of forcing and on combinatorial set theory, in particular on combinatorial problems that seem to raise fundamental questions about forcing. Forcing is a powerful method for examining the extremes of set theoretic behavior permitted by given axioms of set theory. One uses it to construct models of set theory obeying the axioms, the object being to show that some additional property does not follow from the axioms. If one can show that neither a property nor its opposite follows from the axioms, one has found an independence proof for that property. These are highly prized as illuminating the foundations of set theory and thereby of all mathematics.