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Joan Bagaria

Joan Bagaria

Universitat de Barcelona

Experimental Sciences & Mathematics

Born on 17 August 1958 in Manlleu (Catalonia). Fulbright Fellow at Univ. of California, Berkeley, 1985-87. PhD in Logic and the Methodology of Science, UC Berkeley, 1991. Postdoctoral researcher, UC Berkeley, 1991-92. Associate Professor at several Catalonian universities, 1992-2001. ICREA Research Professor at 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; Simons Foundation Fellow at Isaac Newton Institute, Cambridge, UK, Aug. to Dec. 2015. Director of the Barcelona Research Group on Set Theory (BCNSETS), and coordinator and PI of the UB-based Barcelona Logic Group (BCNLOGIC).

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 of mathematical theories. It is both the theory of infinity and the standard 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 in other areas of logic and mathematics. More interestingly, it is sometimes possible to prove that a given problem cannot be solved using standard mathematical tools, which are embodied in the standard Zermelo-Fraenkel with Choice (ZFC) axioms of Set Theory, and therefore new axioms are needed for its solution. Finding and classifying new axioms, thereby expanding the frontiers of mathematical reasoning, is also an essential part of set theory, and of my work.

Selected research activities

Invited talks

Superstrong and Huge Reflection. Kobe Set Theory Workshop. Kobe (Online). 10 March 2021.

Hyperstationary sets. Keynote address at the conference “Logical Perspectives 2021”. Moscow (Online). 7 June 2021.

Some recent results on Structural Reflection. Bristol Logic and Set Theory Seminar / Oxford Set Theory Seminar (Online). 16 July 2021.

Huge Reflection, and Beyond. New York Set Theory Seminar (Online). 3 September 2021.


Managerial activities

Co-organizer of the Set Theory section, Logic Colloquium (European Summer Meeting of the Association for Symbolic Logic). July 19-23, 2021. Poznan (Poland), and Online.

Chairman of the Program Committee of the 2022 European Set Theory Conference (ESTC), to be held August 29-September 2 in Torino.

Appointed Member of the Joint Editorial Board of the Bulletin and the Journal of the London Mathematical Society.

ICREA Memoir 2021