Carrie Knolls, Pure Mathematics Department, University of Waterloo
"Back and forth relations - Part II"
We will prove that, for all countable ordinals β, there is a natural connection between the back-and-forth relation ≤β and the Πβ and Σβ formulas. This result suggests that, in general, it is difficult to “compute” the relations ≤β. For practical purposes, we would like to consider structures where the back-and-forth relations are c.e. which leads us to the notion of α-friendly structures.