Tuesday, November 7, 2017, 17:15

Wrocław University of Technology, 215 D-1

Speaker: Barnabas Farkas (TU Wien)

Title: Cardinal invariants versus towers in analytic P-ideals / An application of matrix iteration

Abstract:

I will present two models concerning interactions between the existence of towers in analytic P-ideals and their cardinal invariants. It is trivial to see that if there is no tower in $\mathcal{I}$, then $\mathrm{add}^*(\mathcal{I})<\mathrm{cov}^*(\mathcal{I})$. I will prove that this implication cannot be reversed no matter the value of $\mathrm{non}^*(\mathcal{I})$. More precisely, let $\mathcal{I}$ be an arbitrary tall analytic P-ideal, I will construct the following two models:

Model1 of $\mathrm{non}^*(\mathcal{I})=\mathfrak{c}$,

there is a tower in $\mathcal{I}$, and $\mathrm{add}^*(\mathcal{I})<\mathrm{cov}^*(\mathcal{I})$. Method: Small filter iteration.

Model2 of $\mathrm{non}^*(\mathcal{I})<\mathfrak{c}$,

there is a tower in $\mathcal{I}$, and $\mathrm{add}^*(\mathcal{I})<\mathrm{cov}^*(\mathcal{I})$. Method: Matrix iteration.

This is a joint work with J. Brendle and J. Verner.