Fred Galvin
Encyclopedia
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
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
.
He invented doublemove chess.
University of Kansas
The University of Kansas is a public research university and the largest university in the state of Kansas. KU campuses are located in Lawrence, Wichita, Overland Park, and Kansas City, Kansas with the main campus being located in Lawrence on Mount Oread, the highest point in Lawrence. The...
. His research interests include set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
and combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
.
His notable combinatorial work includes the proof of the Dinitz conjecture
Dinitz conjecture
In combinatorics, the Dinitz conjecture is a statement about the extension of arrays to partial Latin squares, proposed in 1979 by Jeff Dinitz, and proved in 1994 by Fred Galvin....
. In set theory, he proved with András Hajnal
András Hajnal
András Hajnal is an emeritus professor of mathematics at Rutgers University and a member of the Hungarian Academy of Sciences known for his work in set theory and combinatorics.-Biography:Hajnal was born on 13 May 1931, in Hungary....
that if ℵω1 is a strong limit cardinal
Limit cardinal
In mathematics, limit cardinals are certain cardinal numbers. A cardinal number λ is a weak limit cardinal if λ is neither a successor cardinal nor zero. This means that one cannot "reach" λ by repeated successor operations...
, then
Saharon Shelah
Saharon Shelah is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey.-Biography:...
to the invention of PCF theory
PCF theory
PCF theory is the name of a mathematical theory, introduced by Saharon , that deals with the cofinality of the ultraproducts of ordered sets. It gives strong upper bounds on the cardinalities of power sets of singular cardinals, and has many more applications as well...
. Galvin gave an elementary proof of the Baumgartner–Hajnal theorem
(). The original proof by Baumgartner and Hajnal used forcingForcing (mathematics)
In the mathematical discipline of set theory, forcing is a technique invented by Paul Cohen for proving consistency and independence results. It was first used, in 1963, to prove the independence of the axiom of choice and the continuum hypothesis from Zermelo–Fraenkel set theory...
and absoluteness. Galvin and Shelah also proved the square bracket partition relations
and . Galvin also proved the partition relation where η denotes the order typeOrder type
In mathematics, especially in set theory, two ordered sets X,Y are said to have the same order type just when they are order isomorphic, that is, when there exists a bijection f: X → Y such that both f and its inverse are monotone...
of the set of rational numbers.
Galvin and Prikry proved that every Borel set
Borel algebra
In mathematics, a Borel set is any set in a topological space that can be formed from open sets through the operations of countable union, countable intersection, and relative complement...
is Ramsey. Galvin and Komjáth
Péter Komjáth
Péter Komjáth is a Hungarian mathematician, working in set theory, especially combinatorial set theory. Komjáth is a professor at the Eötvös Loránd University....
showed that the axiom of choice is equivalent to the statement that every graph
Graph (mathematics)
In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges...
has a chromatic number.
Galvin received his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in 1967 from the University of Minnesota
University of Minnesota
The University of Minnesota, Twin Cities is a public research university located in Minneapolis and St. Paul, Minnesota, United States. It is the oldest and largest part of the University of Minnesota system and has the fourth-largest main campus student body in the United States, with 52,557...
.
He invented doublemove chess.