# Boolean ultrapowers in set theory

## Gunter Fuchs

### The City University of New York

Boolean ultrapowers can serve to explain phenomena that arise in the context of iterated ultrapowers, such as the genericity of the critical sequence over the direct limit model. The examples we give are ultrapowers formed using the complete Boolean algebras of Prikry forcing, Magidor forcing, or a generalization of Prikry forcing. Boolean ultrapowers can also be viewed as a direct limit of ultrapowers, and we present some criteria for when the intersection of these ultrapowers is equal to the generic extension of the Boolean ultrapower, thus arriving at a generalization of a phenomenon first observed by Bukovsky and Dehornoy in the context of Prikry forcing.

Gunter Fuchs is a professor at The City University of New York, and conducts research in mathematical logic and especially set theory.