Time:  12:30  13:30 
Room: 
Wean Hall 7201

Speaker: 
Jacob Davis Department of Mathematical Sciences CMU 
Title: 
Some results in settheoretic geology

Abstract:  Given V a universe of set theory, we might be interested in whether it was formed by forcing from some smaller inner universe; such an inner universe is called a ground of V, and the intersection of all such universes is called the mantle ofV. Alternatively we can access a larger class of universes by moving to some forcing extension V[G] and then taking a ground of V[G]. A universe that can be reached in this way is called a generic ground of V, and the intersection of all such universes is the generic mantle of V. It is clear that all grounds are generic grounds, and so the generic mantle of V must be a subclass of its mantle. It is much less clear, and indeed an open question, whether the mantle and generic mantle are necessarily equal. We shall explore some results in this direction. 