Wolfgang Wohofsky, University of Vienna
Distributivity spectrum and fresh functions
We discuss different notions of a distributivity spectrum of forcings.
In the first talk, I will mainly focus on the notion of fresh functions and the corresponding spectrum. A function with domain lambda is fresh if it is new but all its initial segments are in the ground model. I will give general facts how to compute the fresh function spectrum, also discussing what sets are realizable as a fresh function spectrum of a forcing. Moreover, I will provide several examples, including well-known tree forcings on omega such as Sacks and Mathias forcing, as well as Prikry and Namba forcing to illustrate the difference between fresh functions and fresh subsets.
In the second talk, I will also discuss another ('combinatorial') distributivity spectrum; most importantly, analyzing this notion for the forcing P(omega)/fin.
This is joint work with Vera Fischer and Marlene Koelbing.