{{short description|American mathematician}} {{BLP one source |date=April 2024}} '''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<sub>ω<sub>1</sub></sub> is a [[limit cardinal|strong limit cardinal]], then
: <math>2^{\aleph_{\omega_1}}<\aleph_{(2^{\aleph_1})^+}</math>
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]] <math>\omega_1\to(\alpha)^2_k</math> (<math>\alpha<\omega_1, k<\omega</math>). The original proof by [[James Earl Baumgartner|Baumgartner]] and Hajnal used [[Forcing (mathematics)|forcing]] and absoluteness. Galvin and Shelah also proved the square bracket partition relations <math>\aleph_1\not\to[\aleph_1]^2_4</math> and <math>2^{\aleph_0}\not\to[2^{\aleph_0}]^2_{\aleph_0}</math>. Galvin also proved the partition relation <math>\eta\to[\eta]^2_3</math> where η denotes the [[order type]] of the set of rational numbers. Galvin and [[Karel Prikry]] proved that every [[Borel algebra|Borel set]] is Ramsey. Galvin and [[Péter Komjáth|Komjáth]] showed that the [[axiom of choice]] is equivalent to the statement that every [[Graph (discrete mathematics)|graph]] has a [[graph coloring#Chromatic number|chromatic number]].
Galvin received his [[Ph.D.]] in 1967 from the [[University of Minnesota]].<ref name=phd>{{MathGenealogy|id=61007}}</ref>
He also invented [[Marseillais chess]] in 1957 (already published by others earlier in 1925), and Push Chess in 1967.
==References== <references/>
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{{DEFAULTSORT:Galvin, Fred}} [[Category:Living people]] [[Category:20th-century American mathematicians]] [[Category:21st-century American mathematicians]] [[Category:Combinatorialists]] [[Category:Set theorists]] [[Category:University of Minnesota alumni]] [[Category:University of Kansas faculty]] [[Category:Year of birth missing (living people)]]
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