Frederick Rowbottom
Encyclopedia
Frederick Rowbottom was a British
logician and mathematician
. The large cardinal notion of Rowbottom cardinal
s is named after him.
at the University of Wisconsin–Madison
, earning his Ph.D.
degree in 1964, with a thesis entitled Large Cardinals and Small Constructible Sets, under the supervision of Jerome Keisler. With a recommendation from Georg Kreisel
, he took a position at the University of Bristol
in 1965, where he spent the rest of his professional career.
He published a paper called "Some strong axioms of infinity incompatible with the axiom of constructibility" in the Annals of Mathematical Logic, 3 1971. This paper, together with his thesis, "showed that Ramsey cardinals were weaker than measurable cardinals, and that their existence implied the constructible real continuum was countable; he further proved that this followed also from weaker partition and two cardinal properties." The large cardinal notion of Rowbottom cardinal
s is named after him, as is the notion of a Rowbottom ultrafilter
.
Keith Devlin
studied set theory
under Rowbottom. In 1992 he and a student, Jonathan Chapman, wrote a textbook on topos theory, Relative Category Theory and Geometric Morphisms: A Logical Approach, published in Oxford Logic Guides, No. 16. Rowbottom retired in 1993 at the age of 55.
Rowbottom died of heart failure in Hadfield
, England, on 12 October 2009, aged 71.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
logician and mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. The large cardinal notion of Rowbottom cardinal
Rowbottom cardinal
In set theory, a Rowbottom cardinal, introduced by , is a certain kind of large cardinal number.An uncountable cardinal number κ is said to be Rowbottom if for every function f: [κ]...
s is named after him.
Biography
After graduating from Cambridge University, Rowbottom studied under Howard Jerome KeislerHoward Jerome Keisler
H. Jerome Keisler is an American mathematician, currently professor emeritus at University of Wisconsin–Madison. His research has included model theory and non-standard analysis.His Ph.D...
at the University of Wisconsin–Madison
University of Wisconsin–Madison
The University of Wisconsin–Madison is a public research university located in Madison, Wisconsin, United States. Founded in 1848, UW–Madison is the flagship campus of the University of Wisconsin System. It became a land-grant institution in 1866...
, earning 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...
degree in 1964, with a thesis entitled Large Cardinals and Small Constructible Sets, under the supervision of Jerome Keisler. With a recommendation from Georg Kreisel
Georg Kreisel
Georg Kreisel FRS is an Austrian-born mathematical logician who has studied and worked in Great Britain and America. Kreisel came from a Jewish background; his family sent him to England before the Anschluss, where he studied mathematics at Trinity College, Cambridge and then, during World War...
, he took a position at the University of Bristol
University of Bristol
The University of Bristol is a public research university located in Bristol, United Kingdom. One of the so-called "red brick" universities, it received its Royal Charter in 1909, although its predecessor institution, University College, Bristol, had been in existence since 1876.The University is...
in 1965, where he spent the rest of his professional career.
He published a paper called "Some strong axioms of infinity incompatible with the axiom of constructibility" in the Annals of Mathematical Logic, 3 1971. This paper, together with his thesis, "showed that Ramsey cardinals were weaker than measurable cardinals, and that their existence implied the constructible real continuum was countable; he further proved that this followed also from weaker partition and two cardinal properties." The large cardinal notion of Rowbottom cardinal
Rowbottom cardinal
In set theory, a Rowbottom cardinal, introduced by , is a certain kind of large cardinal number.An uncountable cardinal number κ is said to be Rowbottom if for every function f: [κ]...
s is named after him, as is the notion of a Rowbottom ultrafilter
Ultrafilter
In the mathematical field of set theory, an ultrafilter on a set X is a collection of subsets of X that is a filter, that cannot be enlarged . An ultrafilter may be considered as a finitely additive measure. Then every subset of X is either considered "almost everything" or "almost nothing"...
.
Keith Devlin
Keith Devlin
Keith J. Devlin is a British mathematician and popular science writer. He has lived in the USA since 1987 and has dual American-British citizenship.- Biography :...
studied 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...
under Rowbottom. In 1992 he and a student, Jonathan Chapman, wrote a textbook on topos theory, Relative Category Theory and Geometric Morphisms: A Logical Approach, published in Oxford Logic Guides, No. 16. Rowbottom retired in 1993 at the age of 55.
Rowbottom died of heart failure in Hadfield
Hadfield, Derbyshire
Hadfield is a parish and small residential town in High Peak, Derbyshire, England. It lies very close to the River Etherow which forms the border between Derbyshire and Greater Manchester...
, England, on 12 October 2009, aged 71.