#### 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 2023, ‘Steel’s Programme: Evidential Framework, the Core and Ultimate-L’,

*The Review of Symbolic Logic*, 16, 3, 788 – 812.

**Bagaria J**& Wilson TM 2023, ‘The Weak Vopenka Principle for definable classes of structures‘,

*The Journal of Symbolic Logic*, 88, 1, 145 – 168.

**Bagaria J**& Poveda A 2023, ‘More on the preservation of large cardinals under class forcing’,

*The Journal of Symbolic Logic*, 88, 1, 290 – 323.

**Bagaria J**& da Silva SG 2023

*, ‘*w

_{1}-strongly compact cardinals and normality’,

*Topology and its Applications*. Volume 323, 108276.

**Bagaria J**& Lücke P 2023, ‘Huge Reflection‘,

*Annals of Pure and Applied Logic*, Volume 174, Issue 1, 103171.

**Bagaria J**2023, ‘Large cardinals as principles of structural reflection‘,

*Bulletin Of Symbolic Logic*, 29, 1, pp 19 – 70.

#### Selected research activities

**Invited researcher at:**

**Invited talks:**

**Managerial activities:**