Jensen completed the BA in economics 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.
In 2015 the European Set Theory Society awarded him and John R. Steel the Hausdorff medal for their paper "K without a measurable".
Jensen's better-known results include the:
- Axiomatic set theory NFU, a variant of New Foundations (NF) where extensionality is weakened to allow several sets with no elements, and the proof of NFU's consistency relative to Peano arithmetic;
- Fine structure theory of the constructible universe 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 for his 1972 paper titled "The fine structure of the constructible hierarchy";
- Definitions and proofs of various infinitary combinatorial principles in L, including diamond , square, and morass;
- Jensen's covering theorem for L;
- General theory of core models and the construction of the ;
- Consistency of CH plus Suslin's hypothesis.
- Technique of .
- Jensen's page at the Humboldt-Universität zu Berlin.
- Brief biographies of past presidents of the Kurt Gödel Society.