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'''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 <center><math>2^{\aleph_{\omega_1}}<\aleph_{(2^{\aleph_1})^+}</math></center>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|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 (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 invented [[chess variant#Multimove variants|doublemove chess]]. | |||
==References== | |||
<references/> | |||
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{{Persondata | |||
|NAME = Galvin, Frederick William | |||
|ALTERNATIVE NAMES = | |||
|SHORT DESCRIPTION = Mathematician | |||
|DATE OF BIRTH = | |||
|PLACE OF BIRTH = | |||
|DATE OF DEATH = | |||
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}} | |||
{{DEFAULTSORT:Galvin, Fred}} | |||
[[Category:Living people]] | |||
[[Category:20th-century mathematicians]] | |||
[[Category:21st-century mathematicians]] | |||
[[Category:Combinatorialists]] | |||
[[Category:Set theorists]] | |||
[[Category:University of Minnesota alumni]] | |||
[[Category:University of Kansas faculty]] | |||
{{US-mathematician-stub}} | |||
Revision as of 00:42, 30 October 2013
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 ℵω1 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 (). The original proof by Baumgartner and Hajnal used forcing and absoluteness. Galvin and Shelah also proved the square bracket partition relations and . Galvin also proved the partition relation where η denotes the order type of the set of rational numbers.
Galvin and Prikry proved that every Borel set is Ramsey. Galvin and Komjáth showed that the axiom of choice is equivalent to the statement that every graph has a chromatic number.
Galvin received his Ph.D. in 1967 from the University of Minnesota.[1]
He invented doublemove chess.
References
- ↑ 50 yr old Print Journalist Broadbent from Deep River, has hobbies and interests which includes r/c helicopters, property developers in singapore house for rent and scrabble. Suggests that you go to Tomb of Askia.