Advanced Topics in Mathematical Logic

(SoSe 2020)

(SoSe 2020)

The lecture takes place on Fridays from 8:45am to 11:00am in the lecture room of the Kurt Gödel Research Center (Augasse 2-6, 5th floor, green area D, seminar room 5.48). Lectures start on March 6th. Please check u:find to see in which weeks there are no lectures.

Due to the COVID-19 related closure of the University of Vienna this class takes place virtually on moodle. Please, check out the moodle page for further information.

Details about the contents of each lecture can be found here.

The examination of this part of the class will be based on a written summary that needs to be submitted via moodle by May 08, 2020.

### Contents

The first and second part of this class cover different material.The first part (held by Sandra Müller) covers the basic theory of determinacy. We will introduce the concept, discuss important consequences e.g. related to descriptive set theory and, if time allows, go into the connection with large cardinal theory.

The second part (held by Vera Fischer) will focus on the notion of properness. The class of proper forcing notions is an important class of partial orders. We will consider preservation of properness, as well as the preservation of selected properties in proper forcing iterations.

Some knowledge of set theory will be required.

### References for the first part

- Kanamori, A. (2008).
*The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings*. Springer. - Schindler, R. (2014).
*Set Theory: Exploring Independence and Truth*. Springer International Publishing. - Kechris, A. S. (1995).
*Classical Descriptive Set Theory*. Springer, New York. - Koellner, P., & Woodin, W. H. (2010). Large Cardinals from Determinacy. In M. Foreman & A. Kanamori (Eds.),
*Handbook of Set Theory*. Springer.