Profile

I am a mathematical logician, interested in the foundations of mathematics. I got my first university degree at Faculdade de Ciências da Universidade de Lisboa (FCUL) and got a PhD degree from The Pennsylvania State University (USA). My academic career has been wholly within FCUL. I was, for a trimester, Tinker Visiting Professor at Stanford University and, for a semester, Fulbright Scholar at Harvard University. I was Silver Medal in the senior category of the Kurt Gödel Research Prize Fellowship in 2008. I supervised 6 doctoral students and 15 master students.

My research has three main components. Arguably, the most important paper that I wrote was published in 2005, on a new functional interpretation (which can remove some false “ideal elements” from mathematical proofs following, broadly, Hilbert’s programme). I continue to work on these matters since I believe that there are still issues to investigate and to make more widely known. Also in 2005, I published another paper, this one introducing the so-called system of atomic polymorphism. This work has been having some impact, specially among portuguese logicians. Finally, I have a steady interest in Frege’s logicist programme.

My work on “ideal elements” has roots in my PhD thesis. At the time, I worked on weak subsystems of arithmetic related to computational complexity, and my research was mainly on these topics until 2005. In 2008, I wrote in the journal MIND a somewhat influential and critical paper regarding the thesis of bilateralism (a thesis which defends a symmetry between assertion and denial). I also wrote two papers on the conception of truth in Parmenides and Plato. These papers remain ignored.

I have been writing notes for the classes that I teach. These writings already originated two books (written in portuguese): one in Discrete Mathematics, another in Set Theory.