Set Theory - Constructibility

(SoSe 2023)

(SoSe 2023)

This lecture will be an introduction to set theory, in particular to independence proofs. The goal is to establish the consistency of the continuum hypothesis from ZFC. We will start from the ZFC axioms and introduce ordinals and cardinals. Then we will define Gödel's constructible universe $L$ and show that it is a model of ZFC and GCH, the generalized continuum hypothesis. Furthermore, we will introduce measurable cardinals and show that they cannot exist in $L$. If time allows, we will discuss variants $L[U]$ of $L$ which allow the existence of a measurable cardinal.

The lecture takes place

**Fridays 12:15 - 13:45**in the Dissertantenraum (TU Wien Freihaus, green area, 8th floor), starting March 1, 2023.

Depending on what the participants prefer, the lecture can be given in English or in German. There will be lecture notes (Skript) available on TUWEL.