# Prikry-type sequences, iterations and critical sequences

## Gunter Fuchs

### The City University of New York

I will present some old, some new and some classic results on the kinds of sequences which are added by some forcings which are related to Prikry forcing, in some sense. After finding combinatorial properties characterizing these sequences, I will show how to iterate the universe in such a way that the critical sequence of that iteration will satisfy that combinatorial property with respect to the target model, rendering it generic. This connection enables us to analyze precisely the collection of generic sequences which are present in one specific forcing extension. Time permitting, I will also explore connections to Boolean ultrapowers.

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