Mathematical Sciences: Combinatorial Set Theory and Forcing

鲍姆加特纳教授将研究组合集合论， 关于强迫理论和类属集合的问题。 研究领域包括划分演算中的问题 涉及假设CH的ω-3的性质，重点是 在ZFC+CH中可证明的性质以及 附带的独立性问题;与分治有关的问题 序数，极化配分关系和配分关系 对于集合;关于闭无界集合的大小问题;以及 与测度和测度有关的“基数不变量”问题 范畴理论和二次空间理论。 集合论是所有数学的基础。 重要的问题涉及所有数的基本公理 系统，代数，几何和分析，是某些公理 有必要吗？ 在某些情况下，它们是无关紧要的吗？ 在这方面特别重要的是连续体 假设（CH）。 理解它在数学中的作用 激发了20世纪一些最深刻的调查 世纪。

Professor Baumgartner will work in combinatorial set theory, on questions connected to the theory of forcing and generic sets. Areas of research include problems in the partition calculus involving properties of omega-3 assuming CH, focusing on properties provable in ZFC+CH together with the necessarily attendant independence questions; related problems on partition ordinals, polarized partition relations and partition relations for sets; problems on the sizes of closed unbounded sets; and problems on "cardinal invariants" connected both with measure and category theory and with the theory of quadratic spaces. Set theory lies at the foundation of all mathematics. Important questions concern the axioms that underly all number systems, algebra, geometry and analysis, Are certain axioms necessary? Are they irrelevant in certain contexts? Particularly significant in this regard is the Continuum Hypothesis (CH). Understanding its role in mathematics has inspired some of the most profound investigations of the 20th century.