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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]].
| | Nice to meet you, my title is Ling and I totally dig that title. Interviewing is what she does but soon she'll be on her own. Her husband and her chose to reside in Alabama. To play croquet is the pastime I will by no means stop doing.<br><br>Here is my blog; [http://Www.Sceltic.at/index.php?mod=users&action=view&id=19873 sceltic.at] |
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| 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.
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| 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]].
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| Galvin received his [[Ph.D.]] in 1967 from the [[University of Minnesota]].<ref name=phd>{{MathGenealogy|id=61007}}</ref>
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| He invented [[chess variant#Multimove variants|doublemove chess]].
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| ==References==
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| <references/>
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| <!-- Metadata: see [[Wikipedia:Persondata]] -->
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| {{Persondata
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| |NAME = Galvin, Frederick William
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| |SHORT DESCRIPTION = Mathematician
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| {{DEFAULTSORT:Galvin, Fred}}
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| [[Category:Living people]]
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| [[Category:20th-century mathematicians]]
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| [[Category:21st-century mathematicians]]
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| [[Category:Combinatorialists]]
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| [[Category:Set theorists]]
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| [[Category:University of Minnesota alumni]]
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| [[Category:University of Kansas faculty]]
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| {{US-mathematician-stub}}
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Nice to meet you, my title is Ling and I totally dig that title. Interviewing is what she does but soon she'll be on her own. Her husband and her chose to reside in Alabama. To play croquet is the pastime I will by no means stop doing.
Here is my blog; sceltic.at