February 2019
Barnabas Farkas: Degrees of destruction
23/02/19 07:54
Tuesday, February 26, 2019 17:15
Room: D1-215
Speaker: Barnabas Farkas (TU Wien)
Title: Degrees of destruction
Abstract. I'm going to present a survey on our results (joint with L. Zdomskyy) about the following strong notion of destroying Borel ideals: We say that the forcing notion \(\mathbb{P}\) \(+\)-destroys the Borel ideal \(\mathcal{I}\) if \(\mathbb{P}\) adds an \(\mathcal{I}\)-positive \(\dot{X}\) which has finite intersection with every \( A \in \mathcal{I}\cap V\). I will talk about the following:
Room: D1-215
Speaker: Barnabas Farkas (TU Wien)
Title: Degrees of destruction
Abstract. I'm going to present a survey on our results (joint with L. Zdomskyy) about the following strong notion of destroying Borel ideals: We say that the forcing notion \(\mathbb{P}\) \(+\)-destroys the Borel ideal \(\mathcal{I}\) if \(\mathbb{P}\) adds an \(\mathcal{I}\)-positive \(\dot{X}\) which has finite intersection with every \( A \in \mathcal{I}\cap V\). I will talk about the following:
- Examples when usual destruction (that is, when \(\dot{X}\) required to be infinite only) implies \(+\)-destruction, and when it does not.
- Characterization of those Borel ideals which can be \(+\)-destroyed, in particular, we will see that if \(\mathcal{I}\) can be \(+\)-destroyed then the associated Mathias-Prikry forcing \(+\)-destroys it.
- Characterization of those analytic P-ideals which are \(+\)-destroyed by the associated Laver-Prikry forcing.