ForcingFest Vol. I: Posets

Forcing is, arguably, one of the greatest milestones achieved within set theory. Despite its being around for roughly 60 years, the technique introduced by Paul Cohen has not been deeply studied by philosophers of mathematics. The topic sparked some serious interest only in the last few of years. The latest developments of a modal analysis of forcing and of set-theoretic multiversism due to Joel David Hamkins and Benedikt Löwe generated a new philosophical interest for forcing, which brought out very deep philosophical questions on the nature of the set-theoretical universe. Moreover, the surge of set-theoretic potentialism in the philosophy of set theory made forcing an essential tool for a potentialist account of the infinite.

In light of the new philosophical interest sparked around the topic in the last years, the first ForcingFest will deal with forcing (with posets) and its philosophical applications. The goal is to foster interaction between junior researchers and leading scholars in this new area of research that we may call "Philosophy of Forcing". The expected outcome of the course is twofold: on the one hand, participants are expected to get acknowledged with the basics of forcing in a way that is more suited for philosophers, with links to areas (such as modal logic) that are more familiar to them; on the other hand, the philosophy-driven exposition of the topic aims at highlighting the philosophical interest of the issues that forcing aims at solving.