Barnabas Farkas: Cardinal invariants versus towers in analytic P-ideals / An application of matrix iteration
06/11/17 21:20
Tuesday, November 7, 2017 17:15
Room: D1-215
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.
Room: D1-215
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.