Logic & Set Theory seminar: Around the (un)definability of mad families
19 April 2016, 2.00 PM - 19 April 2016, 3.30 PM
Asger Törnquist, University of Copenhagen
Howard House 4th floor seminar room
Note unusual time!
Recall that a family of infinite subsets of ω is almost disjoint if any two distinct elements of the family intersect finitely; if such a family is maximal under inclusion, it is called a mad family.
One particularly well-known application of Adrian Mathias' study of Ramsey theory and forcing in the paper "Happy Families" is that it gives a proof that no analytic, infinite mad family exists. A few years ago, I found a "classical" descriptive set-theoretic proof of this result, en route to proving that there are no infinite mad families in Solovay's model. The two proofs, Mathias' and mine, look quite different. In this talk, I will try to connect the ideas behind the two proofs, with an eye to settling further questions about the (un-)definability of mad families.