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Bagaria i Pigrau, Joan

ICREA Research Professor at UB (Universitat de Barcelona). Experimental Sciences & Mathematics

Born on 17 August 1958, in Manlleu (Catalonia). PhD in Logic and the Methodology of Science, Univ. of California at Berkeley, 1991. ICREA Research Professor at the Univ. of Barcelona, since 2001. Invited researcher at UC Berkeley, Kobe Univ., National Univ. of Singapore, Kurt Gödel Research Center (Vienna), Univ. Paris VII, CalTech, Mittag-Leffler Institut, Hebrew Univ., Harvard Univ., etc. First President of the European Set Theory Society, 2007-11; ICREA Director’s Scientific Advisor, since 2005; Chairman of the INFTY ESF-Research Networking Programme, 2009-14; Member of the Standing Committee of the Catalan Counsel for the Communication of Science (C4), since 2005. Director of the Barcelona research group on set theory (BCNSETS). He has written over 40 research and survey papers on set theory and its applications to other areas of mathematics. He is regularly invited to international meetings and conferences.

Research Interests

I am a mathematical logician working mainly in set theory, an extremely general theory whose objects of study are the abstract infinite sets. Set theory is the strongest and most encompassing theory ever developed. It is both the mathematical theory of infinity and a foundation for mathematics, in the sense that virtually all of mathematics can be formally reduced to it. I develop and apply sophisticated techniques, such as forcing and large cardinals, towards the solution of hard problems in set theory itself and other areas of mathematics. More interestingly, it is sometimes possible to prove that a given problem cannot be solved using the standard mathematical tools, and therefore new axioms are required for its solution. Finding and classifying new axioms, and thereby expanding the frontiers of mathematical reasoning, is also an essential part of set theory, and of my work.

Key Words

Set theory, logic, foundations and philosophy of mathematics.