Mathematical Sciences: Combinatorial Set Theory and Forcing
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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.
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