Mathematical Sciences: Combinatorial Set Theory and Forcing

点击翻译按钮获取中文摘要

Professor Baumgartner will work in combinatorial set theory, on problems of particular relevance to the theory of forcing and generic sets. Areas of research include combinatorial partition theorems, new notions of "freeness" of set-mappings associated with cardinality computations for closed unbounded subsets (involving also new varieties of box-principles), the structure theory of proper, omega-one-semi-proper and Axiom A partial orderings, generalizations of Martin's Axiom, and the cardinal sequences of superatomic Boolean algebras. These topics are in the foundations of set theory and their study will shed light on the most fundamental building blocks in mathematics.