|Time:|| 12:00 - 13:20
Wean Hall 7201
Department of Mathematical Sciences
Carnegie Mellon University
Normally mathematicians are interested in using forcing to move from the current universe to a large outer one. Here we take the opposite approach and consider inner models that our universe is a forcing extension of, which we call grounds, together with their intersection which we call the mantle. We also examine all the universes that can be obtained by first forcing and then taking grounds; the intersection of these is called the generic mantle. We will discuss the known properties of these objects, together with various questions about them that remain open. If time permits we will also look at the generic HOD, which is the intersection of the HODs of all the generic extensions of our current universe.