Jacob Davis: Set-theoretic geology

Speaker: Jacob Davis (CMU)

Title: Set-theoretic geology.

Abstract: 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.

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