# Generalised Descriptive Set Theory, part II

21.03.2023 15:00 - 16:30

M. Moreno (U Wien)

We have introduced the notions of $$\kappa$$-Borel class, $$\kappa$$-analytic class, $$\kappa$$-analytic-coanalytic class, $$\kappa$$-Borel* class in the previous talk. In descriptive set theory the Borel class, the analytic-coanalytic class, and the Borel* class are the same class, we showed that this doesn't hold in the generalized descriptive set theory.

In this talk, we will show the consistency of "$$\kappa$$-Borel* class is equal to the $$\kappa$$-analytic class". This was initially proved by Hyttinen and Weinstein (former Kulikov), under the assumption V=L. We will show a different proof that shows that this holds in L but also can be forced by a cofinality-preserving GCH-preserving forcing from a model of GCH, but also by a $$<\!\kappa$$-closed $$\kappa^+$$‑cc forcing.

Students at Uni Wien are required to attend in person.

Organiser:

Location:

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

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