Luca Facchinetti
Ph.D XLI
Supervisor: Alberto Marcone
Room: Rizzi A2 50
Mail: facchinetti.luca@spes.uniud.it
Research Project
Reverse mathematics and well-quasi-orders
One of the most interesting discoveries of mathematical logic in the past century is that, “when the theorem is proved from the right axioms, the axioms can be proved from the theorem”. This observation gave rise to reverse mathematics, a broad research program in the foundations of mathematics, whose main goal is to find the exact minimal axioms needed to prove the theorems of ordinary mathematics.
Among the topics of interest in reverse mathematics, wqo theory is one of the most prolific. In particular, the equivalent definitions of well-quasi-order are known to have different “computational” strengths. My research focuses on quantifying precisely these strengths, in order to paint a clear picture of the relationships between these definitions.