Mykyta Narusevych, Charles University

Why is it hard to separate T^2_2(R) from T^\infty_2(R) via forcing?

Forcing is a strong model-theoretic tool for proving lower bounds in bounded arithmetic, especially in the context of relativized theories. However, all the known applications work either against the relatively weak theory T^1_2(R) (or some of its extensions) or the rather strong theory T^\infty_2(R), but it is not known what happens in between. The talk is based on an ongoing research targeted towards understanding such a phenomenon.