Born in Manlleu (Catalonia). BA in Philosophy, 1981, and MA in Logic, 1984, Univ. of Barcelona. Fulbright Fellow at UC 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, Univ. of Cambridge, UK, Aug. to Dec. 2015. ASL Gödel Lecture, 2025. Director of the Barcelona Research Group on Set Theory (BCNSETS), and coordinator and PI of the UB-based Barcelona Logic Group.
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 2025, '- Intrinsic Justification for Large Cardinals and Structural Reflection', Philosophia mathematica, 33 - 2 - 123 - 154.
Selected research activities
Invited talks:
Structural reflection and the HOD Conjecture. Four one-hour lectures. Contemporary Set Theory Workshop. Gdansk 24-27 March 2025.
New challenges to our conception of the Higher Infinite. Intelligence – Natural and artificial, relations to Infinity and Reality. 15-17 May 2025. Kankas Manor, Turku (Finland).
Large Cardinals Beyond HOD. The Roaming Logic Conference, Warsaw, 9-11 May 2025
New challenges to our conception of the Higher Infinite. ASL Gödel Lecture. Logic Colloquium 2025. TU Wien. 9 July 2025. Vienna.
Vopěnka’s Principle: From a Practical Joke to a True Axiom of Set Theory. Horizons: Conference in Honour of Petr Vopěnka, Prague, 24-25 October 2025.
Large cardinals beyond HOD. Incompleteness, New Axioms and Truth. Babes, Bolyai University of Cluj-Napoca.
5 December 2025 (Online). Cluj (Romania)
Doctoral Theses supervised:
Marwan Salam Mohammd. Contributions to the Theory of Large Cardinals Beyond Choice. Univ. de Barcelona, Faculty of Mathematics. 30 October 2025.
Luis Alberto Rosa Ferrari. (Co-supervised with Prof. Alfonso Artigue). Some Interactions Between Expansive Dynamics and Mathematical Logic. Universidad de la República. PEDECIBA. Uruguay. 23 December 2025.