# About me.

I am a set theorist and my main research interests lie in the areas of inner model theory, determinacy axioms and descriptive set theory, as well as their relationships and connections to other areas of logic. I am very glad to lead and work with this fantastic group of researchers.

I am currently Assistant Professor (tenure track) at TU Wien in the Institute for Discrete Mathematics and Geometry and recently received an FWF START Prize for my project *Determinacy and Woodin limits of Woodin cardinals*. The START Prize is the highest award for outstanding young researchers in Austria. You can read an interview I gave about my research and the aims in this START project here (in German, see here for the English version).

© FWF/Anja Koppitsch/Daniel Novotny

On September 26th, 2022, the Austrian Day of Mathematics, I received the Förderungspreis of the ÖMG (Austrian Mathematical Society). The laudatio by Grigor Sargsyan is available here.

In addition, I am the PI of the FWF Elise Richter Fellowship V844 with the project *Long games and determinacy when sets are universally Baire* and the international FWF project I6087 entitled *Classifying Derived Models of the Axiom of Determinacy*.

In April 2022, I have been elected as a member of the Young Academy of the Austrian Academy of Sciences (ÖAW). The Young Academy currently consists of 63 excellent researchers who were elected on the basis of acquired important research awards and fellowships. One main aim of the Young Academy is to support innovative research and strengthen young researchers.

**Key achievements:** Proving a conjecture of Sargsyan on the consistency strength of a model of determinacy in which all sets of reals are universally Baire. Development of a new translation procedure to obtain an iterable inner model with a limit of Woodin and strong cardinals. Analysis of the hereditarily ordinal definable sets HOD in canonical inner models with finitely many Woodin cardinals (with Sargsyan). Determination of the large cardinal strength of determinacy of projective games of length $\omega^2$ (with Aguilera). Analysis of the full Wadge hierarchy under determinacy and application to solve a problem in general topology (with Carroy and Medini).

### Recent and upcoming talks.

29 Aug 2022 » European Set Theory Conference, Turin, Plenary talk

Universally Baire Sets and the Inner Model Program06 Sep 2022 » PhDs in Logic XIII, Turin

Highlights from infinite games, mice, and their connection04 Oct 2022 » Baltic Set Theory Seminar

A stationary-tower-free proof of Woodin's Sealing Theorem08 Nov 2022 » Core Model Seminar

A stationary-tower-free proof of Sealing05 Jan 2023 » Winter Meeting of the ASL with the JMM, Boston, Invited Address

Universally Baire Sets, Determinacy, and Inner Models03 Mar 2023 » 10th Indian Conference on Logic and its Applications (ICLA)

Determinacy Axioms and Large Cardinals07 Mar 2023 » STUK Cambridge

Large Cardinals and Determinacy29 Mar 2023 » Mathematical Colloquium University of Vienna

TBA06 Apr 2023 » Online Logic Seminar

TBA05 May 2023 » Gdansk Logic Conference

TBA03 Jul 2023 » Institute for Mathematical Sciences, Singapore

TBA07 Sep 2023 » British Logic Colloquium, Bristol

TBA12 Nov 2023 » Bedlewo, Poland

TBA

Abstracts for older talks can be found here.

### Most recent publications.

Perfect Subtree Property for Weakly Compact Cardinals

(with Y. Hayut)Lebesgue's density theorem and definable selectors for ideals

(with P. Schlicht, D. Schrittesser, and T. Weinert)Sigma_1-definability at higher cardinals: Thin sets, almost disjoint families and long well-orders

(with P. Lücke)Uniformization and Internal Absoluteness

(with P. Schlicht)HOD in inner models with Woodin cardinals

(with G. Sargsyan)

### Current teaching.

- SoSe 2023 Set Theory - Constructibility
- SoSe 2023 Inner Model Theory Seminar: Extender algebra
- SoSe 2023 Analysis für Informatik und Wirtschaftsinformatik (UE)

### Contact information.

**Address**

Dr. Sandra Müller

Forschungsgruppe Algebra (FG1)

Institut für Diskrete Mathematik und Geometrie, TU Wien

Wiedner Hauptstrasse 8-10/104

1040 Wien

Austria.