# Alejandro Poveda

### Biosketch

- FPU-fellow at Universitat de Barcelona (2016-currently)
- MA in Advanced and Professional Mathematics at Universidad de Murcia (2014- 2015)
- Bachelor of Science in Mathematics at Universitat de València (2009-2014)

I am currently a FPU-fellow at UB working under the supervision of Prof. Joan Bagaria. I am a mathematical logician working in Set Theory: the area of Logic devoted to the abstract study of infinity and the standard foundation for Mathematics. Therefore, Set Theory combines both the mathematical theory of infinity and the formal study of Mathematics itself.

Since Gödel's Incompletedness theorems, we know there are mathematical problems that cannot be solved using mathematical tools. More precisely, there are statements which are not deducible nor refutable by the standard axiomatization for mathematics: ZFC. In this regard, Mathematics is colonized by many problems of this nature, and axiom finding and clasification -and, ultimately, expanding the boundaries of mathematical reasoning- is an essential part of Set theory.

In our research group we work with sophisticated theories and techniques such as the Large Cardinal axioms, and Forcing and Generic Absoluteness principles; in order to determine the universal theory for Set Theory: that is, describing which set-theoretical statements (in particular, mathematical) are true regardless they are mathematically undecidable.

Research interests:

- Large Cardinals
- Forcing
- Generic Absoluteness
- Prikry type forcings
- Omega logic and weak extender models

Research group: Barcelona Research Group in Set Theory

### Selected publications

A. Avilés, A. Poveda, S. Todorcevic, Rosenthal compacta that are premetric of finite degree, *Fundamenta Mathematicae* **239** (2017), 259-278