Ronald Björn Jensen (born April 1, 1936) is an American

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 ...

who lives in Germany, primarily known for his work in

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

and

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 ...

Career

Jensen completed a BA in

economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...

American University The American University (AU or American) is a Private university, private University charter#Federal, federally chartered research university in Washington, D.C., United States. Its main campus spans 90-acres (36 ha) on Ward Circle, in the Spri ...

in 1959, and a Ph.D. in

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

at the

University of Bonn The University of Bonn, officially the Rhenish Friedrich Wilhelm University of Bonn (), is a public research university in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the () on 18 October 1818 by Frederick Willi ...

in 1964. His supervisor was

Gisbert Hasenjaeger Gisbert F. R. Hasenjaeger (1 June 1919 – 2 September 2006) was a German Mathematics, mathematical logician. Independently and simultaneously with Leon Henkin in 1949, he developed a new proof of the Gödel's completeness theorem, completeness t ...

. Jensen taught at

Rockefeller University The Rockefeller University is a Private university, private Medical research, biomedical Research university, research and graduate-only university in New York City, New York. It focuses primarily on the biological and medical sciences and pro ...

, 1969–71, and the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

, 1971–73. The balance of his academic career was spent in Europe at the

, the

University of Oslo The University of Oslo (; ) is a public university, public research university located in Oslo, Norway. It is the List of oldest universities in continuous operation#Europe, oldest university in Norway. Originally named the Royal Frederick Univ ...

, the

University of Freiburg The University of Freiburg (colloquially ), officially the Albert Ludwig University of Freiburg (), is a public university, public research university located in Freiburg im Breisgau, Baden-Württemberg, Germany. The university was founded in 1 ...

, the

University of Oxford The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...

, and the

Humboldt-Universität zu Berlin The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humboldt, ...

, from which he retired in 2001. He now resides in

Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...

. Jensen was honored by the

Association for Symbolic Logic The Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in 1936, and its first president was Curt John Ducasse. The current president of the ASL ...

as the first

Gödel Lecture The Gödel Lecture is an honor in mathematical logic given by the Association for Symbolic Logic, associated with an annual lecture at the association's general meeting. The award is named after Kurt Gödel and has been given annually since 1990. ...

r in 1990. In 2015, the European Set Theory Society awarded him and John R. Steel the

Hausdorff Medal The Hausdorff medal is a mathematical prize awarded every two years by the European Set Theory Society. The award recognises the work considered to have had the most impact within set theory among all articles published in the previous five years. ...

for their paper "K without the measurable".

Results

Jensen's better-known results include the: *

Axiomatic 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 ...

NFU, a variant of

New Foundations In mathematical logic, New Foundations (NF) is a non-well-founded, finitely axiomatizable set theory conceived by Willard Van Orman Quine as a simplification of the theory of types of ''Principia Mathematica''. Definition The well-formed fo ...

(NF) where

extensionality In logic, extensionality, or extensional equality, refers to principles that judge objects to be equality (mathematics), equal if they have the same external properties. It stands in contrast to the concept of intensionality, which is concerned wi ...

is weakened to allow several sets with no elements, and the proof of NFU's

consistency In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T is consistent if there is no formula \varphi such that both \varphi and its negation \lnot\varphi are elements of the set of consequences ...

relative to

Peano arithmetic In mathematical logic, the Peano axioms (, ), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th-century Italian mathematician Giuseppe Peano. These axioms have been used nea ...

; * Fine structure theory of the

constructible universe In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by L, is a particular Class (set theory), class of Set (mathematics), sets that can be described entirely in terms of simpler sets. L is the un ...

L. This work led to his being awarded in 2003 the Leroy P. Steele Prize for Seminal Contribution to Research of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

for his 1972 paper titled "The fine structure of the constructible hierarchy"; *Definitions and proofs of various infinitary combinatorial principles in L, including

diamond Diamond is a Allotropes of carbon, solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Diamond is tasteless, odourless, strong, brittle solid, colourless in pure form, a poor conductor of e ...

\diamondsuit

square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

, and morass; *

Jensen's covering theorem In set theory, Jensen's covering theorem states that if 0# does not exist then every uncountable set of ordinals is contained in a constructible set of the same cardinality. Informally this conclusion says that the constructible universe is clo ...

for L; * General theory of

core model In 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 ...

s and the construction of the Dodd–Jensen core model; * Consistency of the

continuum hypothesis In mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states: Or equivalently: In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this ...

plus Suslin's hypothesis; * Technique of coding the universe by a real.

Selected publications

Articles

* Ronald Jensen, 1969, « On the Consistency of a Slight(?) Modification of Quine's NF », ''Synthese 19'': 250–263. With discussion by Quine. * The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol 4, Issue 3, August 1972, pp. 229–308 * with Anthony J. Dodd: The core model, Annals of Mathematical Logic, vol 20, 1981, pp. 43–75. * with Anthony J. Dodd: The covering lemma for K, Annals of Mathematical Logic, vol 22, 1982, pp. 1–30. * Inner models and large cardinals.

Bulletin of Symbolic Logic Bulletin or The Bulletin may refer to: Periodicals (newspapers, magazines, journals) * ''Bulletin'' (online newspaper), a Swedish online newspaper * ''The Bulletin'' (Australian periodical), an Australian magazine (1880–2008) ** Bulletin Deb ...

vol 1, Issue 4 (1995): 393-407. * with John R. Steel: ''K without the measurable'', The Journal of Symbolic Logic, vol 78, Issue 3, 2013, pp. 708–734.

Books

* ''Modelle der Mengenlehre. Widerspruchsfreiheit und Unabhängigkeit der Kontinuumshypothese und des Auswahlaxioms.'' (Lecture Notes in Mathematics; vol. 37). Springer, Berlin 1967. *as editor with Alexander Pestel: Set theory and model theory: proceedings of an informal symposium held at Bonn, June 1–3, 1979. Berlin; New York: Springer-Verlag, 1981. * with Aaron Beller and Philip Welch
''Coding the Universe.''
Cambridge University Press, Cambridge 1982, .

References

External links

*Jensen'

at the

.
Brief biographies
of past presidents of the Kurt Gödel Society. {{DEFAULTSORT:Jensen, Ronald 1936 births Living people 20th-century American mathematicians 21st-century American mathematicians American expatriates in Germany American logicians American University alumni Hausdorff Medal winners Set theorists University of Bonn alumni