Complete list of publications by topic:


Descriptive set theory


  1. Countable ranks at the first and second projective levels
    with Merlin Carl and Philip Welch, 30 pages, submitted
  2. Uniformization and internal absoluteness
    with Sandra Müller, 13 pages, accepted for Proceedings of the American Mathematical Society, May 2022
  3. Coarse groups, and the isomorphism problem for oligomorphic groups
    with Andre Nies and Katrin Tent, Journal of Mathematical Logic, July 2021 (appeared online)
  4. 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)
  5. Long games and sigma-projective sets
    with Juan P. Aguilera and Sandra Müller, Annals of Pure and Applied Logic, January 2021 (appeared online)
  6. Preserving levels of projective determinacy by tree forcings
    with Fabiana Castiblanco, Annals of Pure and Applied Logic, November 2020 (appeared online)
  7. Borel subsets of the real line and continuous reducibility
    with Daisuke Ikegami and Hisao Tanaka, Fundamenta Mathematicae 244 (2019), 209-241
  8. Continuous reducibility and dimension of metric spaces
    Archive for Mathematical Logic 57, 3 (2018), 329-359
  9. 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
  10. 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
  11. 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
  12. Non-isomorphism invariant Borel quantifiers
    with Fredrik Engström, Proceedings of the American Mathematical Society 139 (2011), 4487-4496
  13. Thin equivalence relations in scaled pointclasses
    with Ralf Schindler, Mathematical Logic Quarterly 57, 6 (2011), 615-620

Forcing, large cardinals, Ramsey theory


  1. Asymmetric cut and choose games
    with Peter Holy, Christopher Turner and Philip Welch, 28 pages, submitted
  2. Forcing axioms via ground model interpretations
    with Christopher Turner, 49 pages, submitted
  3. Canonical truth
    with Merlin Carl, 19 pages, accepted for Axiomathes, June 2022
  4. 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)
  5. 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
  6. Sufficient conditions for the forcing theorem, and turning proper classes into sets
    with Peter Holy and Regula Krapf, Fundamenta Mathematicae 246 (2019), 27-44
  7. Characterizations of pretameness and the Ord-cc
    with Peter Holy and Regula Krapf, Annals of Pure and Applied Logic 169, 8 (2018), 775-802
  8. A hierarchy of Ramsey-like cardinals
    with Peter Holy, Fundamenta Mathematicae 242 (2018), 49-74
  9. Choiceless Ramsey Theory for Linear Orders
    with Philipp Lücke and Thilo Weinert, Order 34, 3 (2017), 369-418
  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. 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


  1. Generalized Polish spaces at regular uncountable cardinals
    with Claudio Agostini and Luca Motto Ros, 42 pages, submitted
  2. 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
  3. Descriptive properties of higher Kurepa trees
    with Philipp Lücke, 16 pages, accepted for Research Trends in Contemporary Logic
  4. Measurable cardinals and good Sigma_1(kappa)-wellorderings
    with Philipp Lücke, Mathematical Logic Quarterly 64, 3 (2018), 207-217
  5. Perfect subsets of generalized Baire spaces and long games
    Journal of Symbolic Logic 82, 4 (2017),1317-1355
  6. Sigma_1(kappa)-definable subsets of H(kappa^+)
    with Philipp Lücke and Ralf Schindler, Journal of Symbolic Logic 82, 3 (2017), 1106-1131
  7. The Hurewicz dichotomy for generalized Baire spaces
    with Luca Motto Ros and Philipp Lücke, Israel Journal of Mathematics 216, 2 (2016), 973-1022
  8. Generalized Choquet spaces
    with Samuel Coskey, Fundamenta Mathematicae 232 (2016), 227-248
  9. 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


  1. Decision times of infinite computations
    with Philipp Welch and Merlin Carl, 11 pages, accepted for Notre Dame Journal of Formal Logic in February 2022
  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

Unpublished notes:


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

Theses:


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