Jacob Davis: Some results in set-theoretic geology

Mathematical logic seminar – November 10, 2015
Time:     12:30 – 13:30

Room:     Wean Hall 7201

Speaker:         Jacob Davis
Department of Mathematical Sciences
CMU

Title:     Some results in set-theoretic 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 sub-class 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.

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