### Complete list of publications by topic:

#### Descriptive set theory

- Countable ranks at the first and second projective levels

with Merlin Carl and Philip Welch, 30 pages, submitted - Uniformization and internal absoluteness

with Sandra Müller, 13 pages, accepted for*Proceedings of the American Mathematical Society*, May 2022 - Coarse groups, and the isomorphism problem for oligomorphic groups

with Andre Nies and Katrin Tent,*Journal of Mathematical Logic*, July 2021 (appeared online) -
Lebesgue's density theorem and definable selectors for ideals

with Sandra Müller, David Schrittesser and Thilo Weinert,*Israel Journal of Mathematics*, May 2022 (appeared online) - Long games and sigma-projective sets

with Juan P. Aguilera and Sandra Müller,*Annals of Pure and Applied Logic, January 2021 (appeared online)* - Preserving levels of projective determinacy by tree forcings

with Fabiana Castiblanco,*Annals of Pure and Applied Logic, November 2020 (appeared online)* - Borel subsets of the real line and continuous reducibility

with Daisuke Ikegami and Hisao Tanaka,*Fundamenta Mathematicae 244 (2019), 209-241* - Continuous reducibility and dimension of metric spaces

*Archive for Mathematical Logic 57, 3 (2018), 329-359* - Wadge-like reducibilities in arbitrary quasi-Polish spaces

with Luca Motto Ros and Victor Selivanov,*Mathematical Structures in Computer Science 25 , 8 (2015), 1705-1754* - Lipschitz and uniformly continuous reducibilities on ultrametric Polish spaces

with Luca Motto Ros,*Logic, Computation, Hierarchies, Ontos Mathematical Logic 4(2014), De Gruyter, Berlin, 213-258* - Thin equivalence relations and inner models (correction: Section 3.2 needs the forcings to be ccc in all inner models, noticed by Ralf Schindler)
*Annals of Pure and Applied Logic 165, 10 (2014), 1577-1625*

- Non-isomorphism invariant Borel quantifiers

with Fredrik Engström,*Proceedings of the American Mathematical Society 139 (2011), 4487-4496* - Thin equivalence relations in scaled pointclasses

with Ralf Schindler,*Mathematical Logic Quarterly 57, 6 (2011), 615-620*

#### Forcing, large cardinals, Ramsey theory

- Asymmetric cut and choose games

with Peter Holy, Christopher Turner and Philip Welch, 28 pages, submitted - Forcing axioms via ground model interpretations

with Christopher Turner, 49 pages, submitted - Canonical truth

with Merlin Carl, 19 pages, accepted for*Axiomathes*, June 2022 - How to have more things by forgetting how to count them

with Asaf Karagila,*Proceedings of the Royal Society A, Volume 476, Issue 2239 (2020)* - The exact strength of the class forcing theorem

with Victoria Gitman, Joel David Hamkins, Peter Holy and Kameryn Williams,*Journal of Symbolic Logic*, The Journal of Symbolic Logic, 85, 3 (2020), 869-905 - Sufficient conditions for the forcing theorem, and turning proper classes into sets

with Peter Holy and Regula Krapf,*Fundamenta Mathematicae 246 (2019), 27-44* - Characterizations of pretameness and the Ord-cc

with Peter Holy and Regula Krapf,*Annals of Pure and Applied Logic 169, 8 (2018), 775-802* - A hierarchy of Ramsey-like cardinals

with Peter Holy,*Fundamenta Mathematicae 242 (2018), 49-74* - Choiceless Ramsey Theory for Linear Orders

with Philipp Lücke and Thilo Weinert,*Order 34, 3 (2017), 369-418* - Class forcing, the forcing theorem, and Boolean completions

with Peter Holy, Regula Krapf, Philipp Lücke and Ana Njegomir,*Journal of Symbolic Logic 81, 4 (2016), 1500-1530* - A minimal Prikry-type forcing for singularizing a measurable cardinal

with Karen Räsch and Peter Koepke,*Journal of Symbolic Logic 78, 1 (2013), 85-100*

#### Descriptive set theory at uncountable cardinals

- Generalized Polish spaces at regular uncountable cardinals

with Claudio Agostini and Luca Motto Ros, 42 pages, submitted - Ideal topologies in higher descriptive set theory

with Peter Holy, Marlene Koelbing and Wolfgang Wohofsky,*Annals of Pure and Applied Logic, 173, 4 (2022)*, 36 pages - Descriptive properties of higher Kurepa trees

with Philipp Lücke, 16 pages, accepted for Research Trends in Contemporary Logic - Measurable cardinals and good Sigma_1(kappa)-wellorderings

with Philipp Lücke,*Mathematical Logic Quarterly 64, 3 (2018), 207-217* - Perfect subsets of generalized Baire spaces and long games

*Journal of Symbolic Logic 82, 4 (2017),1317-1355* - Sigma_1(kappa)-definable subsets of H(kappa^+)

with Philipp Lücke and Ralf Schindler,*Journal of Symbolic Logic 82, 3 (2017), 1106-1131* - The Hurewicz dichotomy for generalized Baire spaces

with Luca Motto Ros and Philipp Lücke,*Israel Journal of Mathematics 216, 2 (2016), 973-1022* - Generalized Choquet spaces

with Samuel Coskey,*Fundamenta Mathematicae 232 (2016), 227-248* - Continuous images of closed sets in generalized Baire spaces

with Philipp Lücke,*Israel Journal of Mathematics 209, 1 (2015), 421-461*

#### Higher computability and randomness

- Decision times of infinite computations

with Philipp Welch and Merlin Carl, 11 pages, accepted for Notre Dame Journal of Formal Logic in February 2022 - Reachability for infinite time Turing machines with long tapes

with Benjamin Rin and Merlin Carl,*Logical Methods in Computer Science 16, 2 (2020), 1–16* - Recognizable sets and Woodin cardinals: computation beyond the constructible universe

with Merlin Carl and Philip Welch,*Annals of Pure and Applied Logic 169, 4 (2018), 312-332* - Randomness via infinite computation and effective descriptive set theory

with Merlin Carl,*Journal of Symbolic Logic 83, 2 (2018), 766-789* - Infinite computations with random oracles

with Merlin Carl,*Notre Dame Journal of Formal Logic 58, 2 (2017), 249-270* - The recognizability strength of infinite time Turing machines with ordinal parameters

with Merlin Carl,*Computability in Europe (CiE): Unveiling Dynamics and Complexity, Turku 2017, Lecture Notes in Computer Science 10307 (2017), 198-209* - Tree representations via ordinal machines

with Benjamin Seyfferth,*Computablility 1, 1 (2012), 45-57*

#### Automatic structures

- Ordered Semiautomatic Rings with Applications to Geometry

with Ziyuan Gao, Sanjay Jain, Ji Qi, Frank Stephan and Jacob Tarr,*Language and Automata Theory and Applications (2020), Proceedings* - The isomorphism problem for tree-automatic ordinals with addition

with Sanjay Jain, Bakhadyr Khoussainov, and Frank Stephan,*Information Processing Letters 149 (2019), 19-24* - Automatic learning from repetitive texts

with Rupert Hölzl, Sanjay Jain, Karen Seidel and Frank Stephan,*Algorithmic Learning Theory (ALT), Kyoto 2017, Proceedings of Machine Learning Research 76 (2017), 129-150* - Pumping for ordinal automatic structures

with Alexander Kartzow and Martin Huschenbett,*Computability 6, 2 (2017), 125-164* - Tree-automatic scattered linear orders

with Sanjay Jain, Bakhadyr Khoussainov, and Frank Stephan,*Theoretical Computer Science 626 (2016), 83-96* - Structures without scattered-automatic presentation

with Alexander Kartzow,*Computability in Europe (CiE): The Nature of Computation, Logic, Algorithms, Applications, Milano 2013, Lecture Notes in Computer Science 7921 (2013), 273-283* - Automata on ordinals and automaticity of linear orders

with Frank Stephan,*Annals of Pure and Applied Logic 164, 5 (2013), 523-527* - The mate-in-n problem of infinite chess is decidable

with Dan Brumleve and Joel David Hamkins,*Computability in Europe (CiE): How the world computes, Turing Centenary Conference 2012, Lecture Notes in Computer Science 7318 (2012), 78-88* - Automata on ordinals and linear orders

with Frank Stephan,*Computability in Europe (CiE): Models of Computation in Context, Sofia 2011, Lecture Notes in Computer Science 6735 (2011), 252-259*

### Unpublished notes:

- Iterations of simply definable proper forcings, 2021
- Separation in class forcing extensions with Peter Holy and Regula Krapf, 2017
- Canonical truth with Merlin Carl, 2017
- ZFC without parameters with Ralf Schindler, 2016

### Theses:

- Topics in generalized and classical descriptive set theory (a collection of 8 papers above), Habilitation, Universität Bonn 2017
- Thin equivalence relations in L(R) and inner models Dissertation, Universität Münster 2008