Bounding, splitting, almost disjointness and covering of the meager ideal
Speaker:
Damjan Kalajdzievski
Date and Time:
Friday, September 14, 2018 - 1:30pm to 3:00pm
Location:
Fields Institute, Room 230
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.