Frederick Rowbottom (16 January 1938 – 12 October 2009) was a British

logician Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arg ...

and

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. The

large cardinal In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than the least ...

notion of

Rowbottom cardinal In set theory, a Rowbottom cardinal, introduced by , is a certain kind of large cardinal number. An uncountable cardinal number \kappa is said to be ''\lambda-Rowbottom'' if for every function ''f'': kappa;sup><ω → λ (wher ...

s is named after him.

Biography

Rowbottom was educated at Glossop Grammar School (now Glossopdale School) in High Peak,

Derbyshire Derbyshire ( ) is a ceremonial county in the East Midlands of England. It borders Greater Manchester, West Yorkshire, and South Yorkshire to the north, Nottinghamshire to the east, Leicestershire to the south-east, Staffordshire to the south a ...

, and

King's College, Cambridge King's College, formally The King's College of Our Lady and Saint Nicholas in Cambridge, is a List of colleges of the University of Cambridge, constituent college of the University of Cambridge. The college lies beside the River Cam and faces ...

, where he graduated with a degree in mathematics in 1960. Upon leaving Cambridge, he studied under

Howard Jerome Keisler Howard Jerome Keisler (born 3 December 1936) 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. advisor was Alfred Tarski a ...

at the

University of Wisconsin–Madison The University of Wisconsin–Madison (University of Wisconsin, Wisconsin, UW, UW–Madison, or simply Madison) is a public land-grant research university in Madison, Wisconsin, United States. It was founded in 1848 when Wisconsin achieved st ...

, earning his

Ph.D. A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

degree in 1964, with a thesis entitled ''Large Cardinals and Small Constructible Sets'', under the supervision of

Jerome Keisler Howard Jerome Keisler (born 3 December 1936) 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. advisor was Alfred Tarski a ...

. With a recommendation from

Georg Kreisel Georg Kreisel FRS (September 15, 1923 – March 1, 2015) was an Austrian-born mathematical logician who studied and worked in the United Kingdom and America. Biography Kreisel was born in Graz and came from a Jewish background; his family s ...

, he took a position at the

University of Bristol The University of Bristol is a public university, public research university in Bristol, England. It received its royal charter in 1909, although it can trace its roots to a Merchant Venturers' school founded in 1595 and University College, Br ...

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 The axiom of constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible. The axiom is usually written as ''V'' = ''L''. The axiom, first investigated by Kurt Gödel, is inconsistent with the pr ...

" in the ''Annals of Mathematical Logic'', 3 1971. This paper, together with his thesis, "showed that

Ramsey cardinal In mathematics, a Ramsey cardinal is a certain kind of large cardinal number introduced by and named after Frank P. Ramsey, whose theorem, called Ramsey's theorem establishes that ω enjoys a certain property that Ramsey cardinals generalize t ...

s were weaker than

measurable cardinal In mathematics, a measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure (mathematics), measure on a cardinal ''κ'', or more generally on any set. For a cardinal ''κ'', ...

s, and that their existence implied the constructible real continuum was

countable In mathematics, a Set (mathematics), set is countable if either it is finite set, finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function fro ...

; he further proved that this followed also from weaker partition and two cardinal properties.". The

notion of

s is named after him, as is the notion of a Rowbottom

ultrafilter In the Mathematics, mathematical field of order theory, an ultrafilter on a given partially ordered set (or "poset") P is a certain subset of P, namely a Maximal element, maximal Filter (mathematics), filter on P; that is, a proper filter on P th ...

Keith Devlin Keith James Devlin (born 16 March 1947) is a British mathematician and popular science writer. Since 1987 he has lived in the United States. He has dual British-American citizenship.

studied

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

under Rowbottom. In 1992 he and a student, Jonathan Chapman, wrote a textbook on

topos theory In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally, on a site). Topoi behave much like the category of sets and possess a notion ...

, ''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, Derbyshire Hadfield is a town in the High Peak, Derbyshire, High Peak of Derbyshire, England, with a population at the 2021 Census of 6,763. It lies on the south side of the River Etherow, near to the border with Greater Manchester, at the western edge of ...

, England, on 12 October 2009, aged 71.

References

{{DEFAULTSORT:Rowbottom, Frederick 1938 births 2009 deaths 20th-century British mathematicians 21st-century British mathematicians British logicians 20th-century British philosophers Set theorists Alumni of King's College, Cambridge University of Wisconsin–Madison alumni