Universitat de Barcelona (UB)
Experimental Sciences & Mathematics
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.