Lecture notes : Recent (and not that recent) forcing techniques on finite support iterations (Iterated Forcing Theory and Cardinal Invariants)

Abstract

These are the lectures notes of the minicourse of three sessions presented by the author in the RIMS 2017 Set Theory Workshop on Iterated Forcing and Cardinal Invariants. We focus on the ideas about how to use forcing techniques on FS iteration to produce models where several cardinal invariants are pairwise different. These techniques will converge at the end in a sketch of the proof of the consistency of a constellation of Cichoń's diagram with 10 different values (the maximum possible) modulo three strongly compact cardinals.