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 PI of the UB-based Group in Logic.

Research interests

I am a mathematical logician working mainly in set theory, an extremely general mathematical 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 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 theories and 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 ZFC axioms of set theory, 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.

Selected publications

- Bagaria J, Gitman V & Schindler R 2017, 'Generic Vopenka's Principle, remarkable cardinals, and the weak Proper Forcing Axiom', Archive For Mathematical Logic, 56, 1-2, 1 - 20.

Selected research activities

Invited talks

Generalized Provability Logics and Large Cardinals. Keynote speaker at the XVIII Brazilian Logic Conference. 8-12 May 2017. Pirenópolis (Brazil).

Large cardinals as reflection principles. A survey. XXI Congreso Colombiano de Matemáticas. 5-9 June 2017. Bogotá (Colombia).

Symmetries in the Set-Theoretic Universe and the Higher Infinite. Keynote speaker at Symmetry 2017. The First International Conference on Symmetry. Barcelona, 16 - 18 October 2017.

Strong Reflection Principles and the Hierarchy of Large Cardinals. British Logic Colloquium 2017. University of Sussex. 8-9 September 2017.

Large Cardinals beyond Choice. 6th European Set Theory Conference. Alfréd Rényi Institute of Mathematics, Budapest. 3-7 July 2017.

Large Cardinals beyond Choice. XXVI incontro dell’Associazione Italiana di Logica e sue Applicazioni. Padova (Italy). 25-28 September 2017.

Symmetries of Infinity. On the Infinite. Institut Henri Poincaré and Sorbonne, Paris.18 - 21 October 2017.


Advanced courses given in international conferences

An Introduction to Hyperstationary Sets. 3 one-hour lectures. Winter School in Abstract Analysis (WS2017). 28 January – 4 February, 2017. Hejnice (Czech Republic).

Large Cardinals as Reflection Principles: A General Framework. 4 one-hour lectures. New directions in the Higher Infinite. ICMS, Edinburgh. 10-14 July 2017.