Jean-Louis Krivine is a French mathematician and logician born on February 5, 1944, in Paris, France. He is well-known for his contributions to mathematical logic, set theory, and category theory.
Krivine studied mathematics at the École Normale Supérieure in Paris and completed his Ph.D. in Mathematics at the University of Paris in 1972. He then went on to work as a researcher at the Centre National de la Recherche Scientifique (CNRS) and held various academic positions throughout his career.
One of Krivine's significant contributions is his work on proof theory and lambda calculus. He developed the classical realizability framework called "Krivine's classical realizability" or "realizability by evaluation." This framework provides a constructive interpretation of classical logic using algorithms and computational models.
In addition to his work on proof theory, Krivine made significant contributions to set theory. He worked on large cardinals, forcing techniques, and independence results in set theory. His research in this area has helped advance our understanding of the foundations of mathematics.
Furthermore, Krivine has also made important contributions to category theory. He introduced the concept of "exact completions" in category theory and developed methods for constructing them. These exact completions have applications in various areas of mathematics, including algebraic geometry and mathematical physics.
Throughout his career, Jean-Louis Krivine has received several awards and honors for his work. He was awarded the Silver Medal of the CNRS in 1981 and was elected as a member of the French Academy of Sciences in 1997.
Overall, Jean-Louis Krivine is a highly respected mathematician known for his pioneering work in proof theory, set theory, and category theory. His research has had a significant impact on various branches of mathematics and continues to inspire new developments in these fields.