Filter reflection is an abstract version of stationary reflection. In this talk we will define filter reflection and different avatars of it. We will show the compatibility with large cardinals, forcing axioms, and V＝L.
We will focus on the case when filter reflection holds and stationary reflaction fails, we will discuss how to force this case.
We will also discuss the failure of filter reflection, how to force the failure and the requierements for it.
If the time allows, some applications can be discussed.
This is joint work with Gabriel Fernandes and Assaf Rinot.