Ronald Jensen
Encyclopedia
Ronald Björn Jensen is an American
mathematician active in Europe
, primarily known for his work in mathematical logic
and set theory
.
at American University
in 1959, and a Ph.D. in mathematics
at the University of Bonn
in 1964. His supervisor was Gisbert Hasenjaeger. Jensen taught at Rockefeller University
, 1969–71, and the University of California, Berkeley
, 1971-73. The balance of his academic career was spent in Europe at the
University of Bonn
, the University of Oslo
, the University of Freiburg, the University of Oxford
, and the Humboldt-Universität zu Berlin, from which he retired in 2001. He now resides in Berlin
.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician active in Europe
Europe
Europe is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...
, primarily known for his work in mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
and 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...
.
Career
Jensen completed the BA in economicsEconomics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
at American University
American University
American University is a private, Methodist, liberal arts, and research university in Washington, D.C. The university was chartered by an Act of Congress on December 5, 1892 as "The American University", which was approved by President Benjamin Harrison on February 24, 1893...
in 1959, and a Ph.D. in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at the University of Bonn
University of Bonn
The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...
in 1964. His supervisor was Gisbert Hasenjaeger. Jensen taught at Rockefeller University
Rockefeller University
The Rockefeller University is a private university offering postgraduate and postdoctoral education. It has a strong concentration in the biological sciences. It is also known for producing numerous Nobel laureates...
, 1969–71, and the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
, 1971-73. The balance of his academic career was spent in Europe at the
University of Bonn
University of Bonn
The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...
, the University of Oslo
University of Oslo
The University of Oslo , formerly The Royal Frederick University , is the oldest and largest university in Norway, situated in the Norwegian capital of Oslo. The university was founded in 1811 and was modelled after the recently established University of Berlin...
, the University of Freiburg, the University of Oxford
University of Oxford
The University of Oxford is a university located in Oxford, United Kingdom. It is the second-oldest surviving university in the world and the oldest in the English-speaking world. Although its exact date of foundation is unclear, there is evidence of teaching as far back as 1096...
, and the Humboldt-Universität zu Berlin, from which he retired in 2001. He now resides in Berlin
Berlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
.
Results
Jensen's better-known results include the:- Axiomatic set theory NFUNew FoundationsIn mathematical logic, New Foundations is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled "New Foundations for Mathematical Logic"; hence the name...
, a variant of New FoundationsNew FoundationsIn mathematical logic, New Foundations is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled "New Foundations for Mathematical Logic"; hence the name...
(NF) where extensionality is weakened to allow several sets with no elements, and the proof of NFU's consistencyConsistencyConsistency can refer to:* Consistency , the psychological need to be consistent with prior acts and statements* "Consistency", an 1887 speech by Mark Twain...
relative to Peano arithmetic; - Fine structure theory of the constructible universeConstructible universeIn mathematics, the constructible universe , denoted L, is a particular class of sets which can be described entirely in terms of simpler sets. It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis"...
L. This work led to his being awarded in 2003 the Leroy P. Steele Prize for Seminal Contribution to Research of the American Mathematical SocietyAmerican Mathematical SocietyThe American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
for his 1972 paper titled "The fine structure of the constructible hierarchy"; - Definitions and proofs of various combinatorial principles in L, including diamondDiamondsuitIn mathematics, and particularly in axiomatic set theory, the diamond principle ◊ is a combinatorial principle introduced by that holds in the constructible universe and that implies the continuum hypothesis...
, square, and morassMorass (set theory)In axiomatic set theory, a mathematical discipline, a morass is an infinite combinatorial structure, used to create "large" structures from a "small" number of "small" approximations...
; - Jensen Covering LemmaCovering lemmaIn mathematics, under various anti-large cardinal assumptions, one can prove the existence of the canonical inner model, called the Core Model, that is, in a sense, maximal and approximates the structure of V...
for L; - General theory of core modelCore modelIn set theory, the core model is a definable inner model of the universe of all sets. Even though set theorists refer to "the core model", it is not a uniquely identified mathematical object. Rather, it is a class of inner models that under the right set theoretic assumptions have very special...
s and the construction of the Dodd–Jensen core model; - Technique of coding the universe by a real.
External links
- Jensen's page at the Humboldt-Universität zu Berlin.
- Brief biographies of past presidents of the Kurt Gödel SocietyKurt Gödel SocietyThe Kurt Gödel Society was founded in Vienna, Austria in 1987. It is an international organization aimed at promoting research primarily on logic, philosophy and the history of mathematics, with special attention to connections with Kurt Gödel, in whose honour it was named.The group also organizes...
.