FG1 Seminar talk

Victoria Fiedler
A tree forcing and the tree it creates

In this presentation, I will present a forcing T; its conditions are well-founded trees. I will prove that this forcing is $\sigma$-closed and hence does not add any new reals.

The forcing T creates a q-point $U_T$ in the extension $V[G]$ (where $G$ is $T$-generic). This q-point is special in the sense that it is an ultrafilter far away from p-points, i.e. $U_T$ has no p-point quotient. A proof for this will not be shown in this presentation, but I will motivate why this is of interest to us.