Set Theory

  • 2018 Dec 19

    Set Theory Seminar - Asaf Karagila (The Morris model)

    2:00pm to 3:30pm


    Ross 63
    Title: The Morris model Abstract: Douglass Morris was a student of Keisler, and in 1970 he announced the following result: It is consistent with ZF that for every \alpha, there is a set A_\alpha which is the countable union of countable sets, and the power set of A_\alpha can be partitioned into \aleph_\alpha non-empty sets. The result was never published, and survived only in the form of a short announcement and an exercise in Jech's "The Axiom of Choice". We go over the proof of this theorem using modern tools, as well as some of its odd implications about "size" and countability.