/
lectern.tv
Play15s30s1x0:00/--:--
DoneWatched
Expand
University of Oxford·Christopher Turner
1:18:24
0:00/1:18:24
Type below to lock the video timestamp, or press S to capture a slide.
Forcing Axioms and Name Principles in Set Theory
An examination of the connections between forcing axioms and name principles, exploring these two expressions of generic filter existence within set theory.
Oxford-Bristol Set Theory Seminar Abstract. Forcing axioms are a well-known way of expressing the concept ”there are filters in V which are close to being generic”. 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.