Gaps in the Generic Multiverse

Asaf Karagila, University of East Anglia. Part of the logic seminar series.

The Bristol model is a model which lies between L and L[c], where c is a Cohen real, and yet it does not equal L(x) for any set x.  This unusual model of set theory does not satisfy the axiom of choice, of course.  We will give a broad strokes survey of the construction of the Bristol model and explore some of the implications of the existence of such a model on the lattice of models of ZF intermediate to a Cohen extension and the generic multiverse in particular.

The full construction can be found in the following paper "The Bristol model: an abyss called a Cohen real".