## Publications

### Selected publications (chosen by venue or citations)

1. How to have more things by forgetting how to count them
with Asaf Karagila, accepted for Proceedings of the Royal Society A
2. Preserving levels of projective determinacy by tree forcings
with Fabiana Castiblanco, accepted for Annals of Pure and Applied Logic
3. The exact strength of the class forcing theorem
with Victoria Gitman, Joel David Hamkins, Peter Holy and Kameryn Williams, to appear in Journal of Symbolic Logic
4. Characterizations of pretameness and the Ord-cc
with Peter Holy and Regula Krapf, Annals of Pure and Applied Logic 169, 8 (2018), 775-802
5. 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
6. Randomness via infinite computation and effective descriptive set theory
with Merlin Carl, Journal of Symbolic Logic 83, 2 (2018), 766-789
7. Perfect subsets of generalized Baire spaces and long games
Journal of Symbolic Logic 82, 4 (2017),1317-1355
8. Sigma_1(kappa)-definable subsets of H(kappa^+)
with Philipp Lücke and Ralf Schindler, Journal of Symbolic Logic 82, 3 (2017), 1106-1131
9. The Hurewicz dichotomy for generalized Baire spaces
with Luca Motto Ros and Philipp Lücke, Israel Journal of Mathematics 216, 2 (2016), 973-1022
10. 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
11. Continuous images of closed sets in generalized Baire spaces
with Philipp Lücke, Israel Journal of Mathematics 209, 1 (2015), 421-461
12. 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
13. Thin equivalence relations and inner models (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
14. Automata on ordinals and automaticity of linear orders
with Frank Stephan, Annals of Pure and Applied Logic 164, 5 (2013), 523-527
15. 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

### Complete list of publications (by topic):

#### Descriptive set theory

1. Coarse groups, and the isomorphism problem for oligomorphic groups
with Andre Nies and Katrin Tent, submitted
2. Lebesgue's density theorem and definable selectors for ideals
with Sandra Müller, David Schrittesser and Thilo Weinert, submitted
3. Long games and sigma-projective sets
with Juan P. Aguilera and Sandra Müller, submitted
4. Preserving levels of projective determinacy by tree forcings
with Fabiana Castiblanco, accepted for Annals of Pure and Applied Logic
5. Borel subsets of the real line and continuous reducibility
with Daisuke Ikegami and Hisao Tanaka, Fundamenta Mathematicae 244 (2019), 209-241
6. Continuous reducibility and dimension of metric spaces
Archive for Mathematical Logic 57, 3 (2018), 329-359
7. 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
8. 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
9. Thin equivalence relations and inner models (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
10. Non-isomorphism invariant Borel quantifiers
with Fredrik Engström, Proceedings of the American Mathematical Society 139 (2011), 4487-4496
11. Thin equivalence relations in scaled pointclasses
with Ralf Schindler, Mathematical Logic Quarterly 57, 6 (2011), 615-620

#### Descriptive set theory in the uncountable

1. Generalized Polish spaces at uncountable regular cardinals
with Claudio Agostini and Luca Motto Ros, in preparation
2. Descriptive properties of higher Kurepa trees
with Philipp Lücke, in preparation
3. Measurable cardinals and good Sigma_1(kappa)-wellorderings
with Philipp Lücke, Mathematical Logic Quarterly 64, 3 (2018), 207-217
4. Perfect subsets of generalized Baire spaces and long games
Journal of Symbolic Logic 82, 4 (2017),1317-1355
5. Sigma_1(kappa)-definable subsets of H(kappa^+)
with Philipp Lücke and Ralf Schindler, Journal of Symbolic Logic 82, 3 (2017), 1106-1131
6. The Hurewicz dichotomy for generalized Baire spaces
with Luca Motto Ros and Philipp Lücke, Israel Journal of Mathematics 216, 2 (2016), 973-1022
7. Generalized Choquet spaces
with Samuel Coskey, Fundamenta Mathematicae 232 (2016), 227-248
8. Continuous images of closed sets in generalized Baire spaces
with Philipp Lücke, Israel Journal of Mathematics 209, 1 (2015), 421-461

#### Forcing, large cardinals, Ramsey theory

1. How to have more things by forgetting how to count them
with Asaf Karagila, accepted
2. The exact strength of the class forcing theorem
with Victoria Gitman, Joel David Hamkins, Peter Holy and Kameryn Williams, to appear in Journal of Symbolic Logic
3. Sufficient conditions for the forcing theorem, and turning proper classes into sets
with Peter Holy and Regula Krapf, Fundamenta Mathematicae 246 (2019), 27-44
4. Characterizations of pretameness and the Ord-cc
with Peter Holy and Regula Krapf, Annals of Pure and Applied Logic 169, 8 (2018), 775-802
5. A hierarchy of Ramsey-like cardinals
with Peter Holy, Fundamenta Mathematicae 242 (2018), 49-74
6. Choiceless Ramsey Theory for Linear Orders
with Philipp Lücke and Thilo Weinert, Order 34, 3 (2017), 369-418
7. 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
8. 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

#### Infinite time computation and randomness

1. Ranks of countable length
with Philipp Welch and Merlin Carl, in preparation
2. 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
3. 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
4. Randomness via infinite computation and effective descriptive set theory
with Merlin Carl, Journal of Symbolic Logic 83, 2 (2018), 766-789
5. Infinite computations with random oracles
with Merlin Carl, Notre Dame Journal of Formal Logic 58, 2 (2017), 249-270
6. 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
7. Tree representations via ordinal machines
with Benjamin Seyfferth, Computablility 1, 1 (2012), 45-57

#### Automatic structures

1. 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
2. The isomorphism problem for tree-automatic ordinals with addition
with Sanjay Jain, Bakhadyr Khoussainov, and Frank Stephan, Information Processing Letters 149 (2019), 19-24
3. 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
4. Pumping for ordinal automatic structures
with Alexander Kartzow and Martin Huschenbett, Computability 6, 2 (2017), 125-164
5. Tree-automatic scattered linear orders
with Sanjay Jain, Bakhadyr Khoussainov, and Frank Stephan, Theoretical Computer Science 626 (2016), 83-96
6. 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
7. Automata on ordinals and automaticity of linear orders
with Frank Stephan, Annals of Pure and Applied Logic 164, 5 (2013), 523-527
8. 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
9. 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