Christopher Turner

Forcing Axioms and Name Principles

Abstract: \textit{Forcing axioms} are a well-known way of expressing the concept ''there are filters in V which are close to being generic". \textit{Name principles} are another expression of this concept. A name principle says: ''Let $\sigma$ be any sufficiently nice name which is forced to have some property. Then there is a filter $g\in V$ such that $\sigma^g$ has that property." Name principles have often been used on an ad-hoc basis in proofs, but have not been studied much as axioms in their own right. In this talk, I will present some of the connections between different name principles, and between name principles and forcing axioms.
This is based on joint work with Philipp Schlicht.