Damjan Kalajdzievski: Bounding, splitting, almost disjointness and covering of the meager ideal

Place: Fields Institute (Room 210)
Date: , 2018 (13:30-15:00)
Speaker: Damjan Kalajdzievski
Title: Bounding, splitting, almost disjointness and covering of the meager ideal
Abstract:This talk is on joint work with Osvaldo Guzman. This talk will go over forcing $\omega_1=\mathfrak{b}=cov(\mathcal{M})<\mathfrak{s}=\omega_2$ with a countable support iteration of proper forcings. In doing so we will introduce the forcings $\mathbb{PT}(\mathcal{F})$, which are Miller trees that satisfy a restriction on splitting nodes relative to the filter $\mathcal(F)$, and discuss their properties when $\mathcal{F}$ is Canjar. The result is achieved by iterating the forcing $\mathbb{F}_\sigma*\mathbb{PT}(\mathcal{F})$, where $\mathbb{F}_\sigma$ is the forcing of $F_\sigma$ filters on $\omega$ ordered by reverse inclusion.

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