# 2020 seminar talk: Forcing the $\Sigma^1_3$-separation property

Talk held by Stefan Hoffelner (University of Münster, North Rhine-Westphalia, Germany) at the KGRC seminar on 2020-06-04.

### Abstract

The separation property, introduced in the 1920s, is a
classical notion in descriptive set theory. It is well-known due to
Moschovakis, that **$\Delta^1_2$**-determinacy implies the
**$\Sigma^1_3$**-separation property; yet
**$\Delta^1_2$**-determinacy implies an inner model with a Woodin
cardinal. The question whether the **$\Sigma^1_3$**-separation
property is consistent relative to just ZFC remained open however
since Mathias' “Surrealist Landscape”-paper. We show that one can
force it over L.

### Time and Place

Talk at 4:00pm via Zoom