Results and Independence Proofs in Combinatorial Set Theory served as the dissertation title for James Earl Baumgartner, who received his PhD from the University of California, Berkeley in 1970. This work established his career in mathematical logic, set theory, and topology, leading to a long tenure as a professor at Dartmouth College.
Academic Trajectory
Born in Wichita, Kansas, in 1943, Baumgartner began his undergraduate education in 1960 at the California Institute of Technology. He later transferred to the University of California, Berkeley, where he completed his doctoral studies under the supervision of Robert Vaught. In 1969, he joined the faculty at Dartmouth College, where he spent his entire professional career teaching and conducting research.
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Baumgartner’s research focused on the complexities of foundations, spanning topics such as Ramsey theory, cardinal arithmetic, iterated forcing, and Axiom A. He provided a consistency proof demonstrating that any two aleph-one-dense sets of real numbers are order isomorphic. Together with András Hajnal, he proved the Baumgartner-Hajnal theorem, which addresses partition relations for cardinal numbers.
Professional Scope
Throughout his career, Baumgartner investigated a diverse array of mathematical structures, including filters, ideals, disjoint refinements, and the chromatic number of graphs. He also contributed to the field through editorial work, notably serving as an editor for the 1990 volume Axiomatic Set Theory, published as part of the Contemporary Mathematics series. His body of work includes numerous papers published between 1975 and 1984.
Fast facts
- Born: 1943, Wichita
- Died: 2011, Hanover (NH)
- PhD: 1970, University of California, Berkeley
- Primary Institution: Dartmouth College
- Fields: Set theory, mathematical logic, topology
Questions readers ask
Where did Baumgartner spend his career?
He served as a professor at Dartmouth College from 1969 until his death in 2011.
What was the focus of his doctoral dissertation?
His 1970 dissertation was titled Results and Independence Proofs in Combinatorial Set Theory.
Achievements
- Held posts at Dartmouth College
- Fields: mathematical logic, set theory and mathematics
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