# Fresh function spectra

05.04.2022 15:00 - 16:30

W. Wohofsky (U Wien)

My talk will be about the notion of fresh function and I will discuss 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, Laver, Miller, and Mathias forcing, as well as Prikry and Namba forcing to illustrate the difference between fresh functions and fresh subsets.

This is joint work with Vera Fischer and Marlene Koelbing.

Organiser:

Location:

#### SR 10, 1. Stock, Koling. 14-16, 1090 Wien

SR 10, 1. Stock, Koling. 14-16, 1090 Wien