Fred Galvin

Frederick William Galvin is a mathematician, currently a professor at the University of Kansas. His research interests include set theory and combinatorics.

His notable combinatorial work includes the proof of the Dinitz conjecture. In set theory, he proved with András Hajnal that if ℵ_ω1 is a strong limit cardinal, then

holds. The research on extending this result led Saharon Shelah to the invention of PCF theory. Galvin gave an elementary proof of the Baumgartner–Hajnal theorem ${\displaystyle \omega _{1}\to (\alpha )_{k}^{2}}$ (${\displaystyle \alpha <\omega _{1},k<\omega }$). The original proof by Baumgartner and Hajnal used forcing and absoluteness. Galvin and Shelah also proved the square bracket partition relations ${\displaystyle \aleph _{1}\not \to [\aleph _{1}]_{4}^{2}}$ and ${\displaystyle 2^{\aleph _{0}}\not \to [2^{\aleph _{0}}]_{\aleph _{0}}^{2}}$. Galvin also proved the partition relation ${\displaystyle \eta \to [\eta ]_{3}^{2}}$ where η denotes the order type of the set of rational numbers.

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