Norwich

Starting with a countable transitive model of V=L, we show that by 
adding a single Cohen real, c, most intermediate models do no satisfy choice. In 
fact, most intermediate models to L[c] are not even definable.

The key part of the proof is the Bristol model, which is intermediate to L[c], 
but is not constructible from a set. We will give a broad explanation of the 
construction of the Bristol model within the constraints of time.

I will talk about two pieces of work on finite covers:

(i) Work of Hrushovski which, for a stable theory, links splitting of certain finite covers with higher amalgamation properties;

(ii) Joint work of myself and Elisabetta Pastori which uses group cohomology to investigate some non-split finite covers of the set of k-sets from a disintegrated set.