Speaker
Gian Marco Osso
Dipartimento di Scienze Matematiche, Informatiche e Fisiche  Università di Udine
Talks at this conference:
Wednesday, 14:50, J335 
The GalvinPrikry theorem in the Weihrauch lattice 
I will address the classification of different fragments of the GalvinPrikry theorem, an infinite dimensional generalization of Ramsey’s theorem, in terms of their uniform computational content (Weihrauch degree). This work can be seen as a continuation of [1], which focused on the Weihrauch classification of functions related to the NashWilliams theorem, i.e., the restriction of the GalvinPrikry theorem to open sets. We have shown that functions related to the GalvinPrikry theorem for Borel sets of rank \(n\) are strictly between the \((n+1)\)th and \(n\)th iterate of the hyperjump operator \(\mathsf{HJ}\), which corresponds to \(\Pi^1_1\)\(\mathsf{CA}_0\) in the Weihrauch lattice. To establish this classification we obtain the following computability theoretic result (along the lines of [2] and [3]): a Turing jump ideal containing homogeneous sets for all \(\Delta^0_{n+1}(X)\) sets must also contain \(\mathsf{HJ}^n(X)\). Similar results also hold for Borel sets of transfinite rank. This is joint work with Alberto Marcone. Bibliography
