• Class Collection versus Class Choice

    I’ve been thinking recently about different versions of Global Choice, which are equivalent in the presence of Powerset but not equivalent in its absence. As part of this I realized that this gives the answer to how different formulations of what I’ve variously seen called Class Choice/Class Collection/Class Bounding relate in the absence of Global Choice.

    [would you like to know more?]

  • Every countable model of set theory end-extends to a model of V = L

    This theorem has popped up in my life a few times in the past week, and it’s one of the coolest results I know of, so I wanted to share it with the world.

    Theorem (Barwise) Every countable transitive model of $\mathsf{ZF}$ has an end-extension to a model of $\mathsf{ZFC} + V = L$.

    [would you like to know more?]

(For blog posts from before summer 2018, see my old site.)