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 help to 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 publications

Bagaria J 2019, ‘Derived topologies on ordinals and stationary reflection’, Transactions of the American Mathematical Society, vol. 371, no. 3, pp 1981-2002.

Bagaria J, Koellner P & Woodin WH 2019, ‘Large Cardinals Beyond Choice’. Bulletin of Symbolic Logic. September 2019, Volume 25, Issue 3, 283-318

Selected research activities

Invited Talks

  • The true universe of sets, Woodin’s HOD Conjecture, very large cardinals, and class forcing. Joint Quest for Absolute Infinity and the Continuum – From Cantor to Woodin. Turku (Finland).
  • On the preservation of very large cardinals under class forcing. Higher Recursion Theory and Set Theory. IMS, National Univ. of Singapore.
  • Philosophical implications of some recent breakthroughs in Set Theory. Set Theory: Bridging Mathematics and Philosophy. Univ. of Konstanz (Germany).
  • On Woodin’s HOD-Conjecture, large cardinals beyond Choice, and class forcing. 12th Panhellenic Logic Symposium. Anogia, Crete (Greece).
  • Some more applications of w1-strongly compact cardinals in General Topology. Third Pan Pacific International Conference on Topology and Applications (3rdPPICTA). Chengdu (China).
  • The Weak Vopenka Principle for definable classes of structures. RIMS Set Theory Workshop. Set Theory and Infinity. RIMS, Univ. of Kyoto (Japan).
  • The Weak Vopenka Principle for definable classes of structures. Di Prisco Fest. Univ. de los Andes, Bogotá (Colombia).
  • Vopenka’s Principle, the Weak Vopenka Principle, and large cardinals. A tutorial. IPM Set Theory Conference. IPM (Tehran).