## Research Areas

### Set Theory

Our research concentrates on set theory, in particular on:

- Constructible inner models
- Large cardinals
- Consistency strength
- Forcing
- Combinatorial Set Theory
- Descriptive set theory and Determinacy

Part of this work is or has been funded by the following projects:

- DFG-NWO Bilateral Cooperation Project Infinitary combinatorics without the axiom of choice (01/11/2007 until 31/10/2010; Apter, Dimitriou, Koepke, Löwe)

### Generalized Computability Theory

- Ordinal computability theory.
- Linking ordinal computations to constructibility theory and descriptive set theory.

This work belongs to the research area Structural and Algorithmic Complexity of the Hausdorff Center for Mathematics.

### Formal Mathematics

- The NAPROCHE project (NAtural language PROof CHEcking), where we study the linguistics and logic of common mathematical language. The project includes the development of a proof-checker with a natural language, LaTeX-quality interface.
- Applying NAPROCHE in the teaching of logic and proving.

Part of this work is funded by the Hausdorff Center for Mathematics through a Hausdorff project "A research platform for natural language orientated formal mathematics".

### General Logic

- Editorial work within the edition of the collected works of Felix Hausdorff: descriptive set theory.