Joan  Bagaria i Pigrau

Joan Bagaria i Pigrau

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), Fields Institute (Toronto), Univ. Paris VII, CalTech, Mittag-Leffler Institut (Sweden), 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, University of Cambridge, UK, 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. 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 all of mathematics can be interpreted and formally reduced to it. I develop sophisticated techniques, such as the method of Forcing for building models of Set Theory and the theory of Large Cardinals, and apply them to the solution of hard problems in Set Theory itself and in other areas of logic and mathematics. Most  interestingly, one can prove sometimes 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 publications

Bagaria J & Ternullo C 2023, ‘Steel’s Programme: Evidential Framework, the Core and Ultimate-L’, The Review of Symbolic Logic, 16, 3, 788 – 812.
Bagaria J & Wilson TM 2023, ‘The Weak Vopenka Principle for definable classes of structures‘, The Journal of Symbolic Logic, 88, 1, 145 – 168.
Bagaria J & Poveda A 2023, ‘More on the preservation of large cardinals under class forcing’, The Journal of Symbolic Logic, 88, 1, 290 – 323.
Bagaria J & da Silva SG 2023, ‘w1-strongly compact cardinals and normality’, Topology and its Applications. Volume 323, 108276.
Bagaria J & Lücke P 2023, ‘Huge Reflection‘, Annals of Pure and Applied Logic, Volume 174, Issue 1, 103171.
Bagaria J 2023, ‘Large cardinals as principles of structural reflection‘, Bulletin Of Symbolic Logic, 29, 1, pp 19 – 70.

Selected research activities

Invited researcher at:
-University of California, Berkeley (USA), April 28 to May 15.
-Fields Institute, Toronto (Canada), June 1-15.
-Kobe University (Japan), October 27 to November 4.
Invited talks:
-Self-similarity in the Higher Infinite. Berkeley Logic Colloquium. May 5.
-Large cardinals as reflection properties of the set-theoretic universe, a tutorial consisting of four 1-hour lectures. RIMS Workshop on Large cardinals and the continuum. RIMS, Kyoto University (Japan). October 23-27.
-Structural Reflection on the edge and beyond. Invited talk at the joint Kobe-Waseda Set Theory Seminar. Kobe University (Japan). November 1.
Managerial activities:
-Co-cordinator (with C. Ternullo) of the workshop “What can Philosophy do for Set Theory?”. Universitat de Barcelona. March 29-31.
-Member of the Joint Editorial Board of the Bulletin and the Journal of the London Mathematical Society.
-Member of the Scientific Advisory Board of the Catalan Mathematical Society.