Joan Bagaria

Universitat de Barcelona (UB)

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 & Shelah S 2016, ‘On partial orderings having precalibre-ℵ1 and fragments of Martin’s axiom’, Fundamenta Mathematicae, 232, 2, 181 – 197.

Bagaria J, Hamkins J, Tsaprounis K & Usuba T 2016, ‘Superstrong and other large cardinals are never Laver indestructible’, Archive for Mathematical Logic, Volume 55, Issue 1, 19-35.

Bagaria J & Väänänen J 2016, ‘On the symbiosis between model-theoretic and set-theoretic properties of large cardinals’, The Journal of Symbolic Logic, 81, 2, 584 – 604.

Selected research activities

Invited talks

On the consistency strength of n-stationarity. Menachem Magidor 70th Birthday Conference. 17-19 February, 2016.  Einstein Institute of Mathematics, Hebrew University, Jerusalem (Israel).

On simplicity and truth, a case study in the theory of large cardinals. Crossing Worlds: Mathematical logic, philosophy, art. 3-4 June 2016, Helsinki (Finland).

Reflection phenomena in the set-theoretic universe. Keynote speaker at the Set Theoretic Pluralism Symposium. 12-17 July 2016. Aberdeen (Scotland)

Doctoral thesis director

Salvador Mancilla, PhD. A Generalization of Stationary Reflection and Large Cardinals. Univ. of Barcelona. Graduated 22 April.

Managerial activities

Member of the Program Committee. Novi Sad Conference in Set theory and General Topology” (SETTOP 2016). June 20-24, 2016, Novi-Sad (Serbia).

Chairman of the organizing and scientific committees of the CRM Intensive Research Programme on Large Cardinals and Strong Logics. September 6 to December 16, Bellaterra (Barcelona). (Resigned in June 2016.)