Publications

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Submitted

• Peter Holy, Philipp Lücke and Sandra Müller. Outward Compactness.
  30 pages, 2024.


• Vincenzo Dimonte, Martina Iannella and Philipp Lücke. Descriptive properties of I2-embeddings.
  21 pages, 2024.

Accepted

• Omer Ben-Neria and Philipp Lücke. On Σ₁-definable closed unbounded sets.
  Accepted for publication in the Canadian Journal of Mathematics. 32 pages, 2024.


• Philipp Lücke. The complexity of non-stationary ideals.
  To appear in a survey volume of the Mathematical Institute of the Serbian Academy of Sciences. 26 pages, 2024.


• Philipp Lücke and Philipp Schlicht. Descriptive properties of higher Kurepa trees.
  To appear in Research Trends in Contemporary Logic (College Publications). 16 pages, 2020.

Published

1. Joan Bagaria and Philipp Lücke. Patterns of Structural Reflection in the large-cardinal hierarchy.
   Transactions of the American Mathematical Society. Volume 377, Issue 5, pp. 3397-3447, 2024.


2. Philipp Lücke and Sandra Müller. Σ₁-definability at higher cardinals: Thin sets, almost disjoint families and long well-orders.
   Forum of Mathematics, Sigma. Volume 11, 36 pages, 2023.


3. Philipp Lücke and Ioannis Souldatos. Non-absoluteness of Hjorth's cardinal characterization.
   Fundamenta Mathematicae. Volume 262, Issue 2, pp. 105-128, 2023.


4. Joan Bagaria and Philipp Lücke. Huge reflection.
   Annals of Pure and Applied Logic. Volume 174, Issue 1, 32 pages, 2023.


5. Sean Cox and Philipp Lücke. Forcing axioms and the complexity of non-stationary ideals.
   Monatshefte für Mathematik. Volume 199, Issue 1, pp. 45-84, 2022.


6. Philipp Lücke. Structural reflection, shrewd cardinals and the size of the continuum.
   Journal of Mathematical Logic. Volume 22, Issue 2, 43 pages, 2022.


7. Philipp Lücke. Strong unfoldability, shrewdness and combinatorial consequences.
   Proceedings of the American Mathematical Society. Volume 150, Issue 9, pp. 4005-4020, 2022.


8. Philipp Lücke and Sandra Müller. Closure properties of measurable ultrapowers.
   Journal of Symbolic Logic. Volume 86, Issue 2, pp. 762-784, 2021.


9. Peter Holy and Philipp Lücke. Small Models, Large Cardinals, and Induced Ideals.
   Annals of Pure and Applied Logic. Volume 172, Issue 2, 50 pages, 2021.


10. Peter Holy, Philipp Lücke and Ana Njegomir. Characterizing large cardinals through Neeman's pure side condition forcing.
    Fundamenta Mathematicae. Volume 252, Issue 1, pp. 53-102, 2021.


11. Philipp Lücke. Partition properties for simply definable colourings.
    Israel Journal of Mathematics. Volume 236, Issue 2, pp. 841-898, 2020.


12. Philipp Lücke. Closed maximality principles and generalized Baire spaces.
    Notre Dame Journal of Formal Logic. Volume 60, Number 2, pp. 253-282, 2019.


13. Peter Holy, Philipp Lücke and Ana Njegomir. Small embedding characterizations for large cardinals.
    Annals of Pure and Applied Logic. Volume 170, Issue 2, pp. 251-271, 2019.


14. Chris Lambie-Hanson and Philipp Lücke. Squares, ascent paths, and chain conditions.
    Journal of Symbolic Logic. Volume 83, Issue 4, pp. 1512-1538, 2018.


15. Philipp Lücke and Philipp Schlicht. Measurable cardinals and good Σ₁(κ)-wellorderings.
    Mathematical Logic Quarterly. Volume 64, Issue 3, pp. 207-217, 2018.


16. Philipp Lücke, Philipp Schlicht and Thilo Weinert. Choiceless Ramsey theory of linear orders.
    Order. Volume 34, Issue 3, pp. 369-418, 2017.


17. Philipp Lücke, Ralf Schindler and Philipp Schlicht. Σ₁(κ)-definable subsets of H(κ⁺).
    Journal of Symbolic Logic. Volume 82, Issue 3, pp. 1106-1131, 2017.


18. Philipp Lücke. Ascending paths and forcings that specialize higher Aronszajn trees.
    Fundamenta Mathematicae. Volume 239, Issue 1, pp. 51-84, 2017.


19. Sean Cox and Philipp Lücke. Characterizing large cardinals in terms of layered posets.
    Annals of Pure and Applied Logic. Volume 168, Issue 5, pp. 1112-1131, 2017.


20. Peter Holy and Philipp Lücke. Simplest possible locally definable well-orders.
    Fundamenta Mathematicae. Volume 236, Issue 2, pp. 101-139, 2017.


21. Peter Holy, Regula Krapf, Philipp Lücke, Ana Njegomir and Philipp Schlicht. Class forcing, the forcing theorem and Boolean completions.
    Journal of Symbolic Logic. Volume 81, Issue 4, pp. 1500-1530, 2016.


22. Philipp Lücke, Luca Motto Ros and Philipp Schlicht. The Hurewicz dichotomy for generalized Baire spaces.
    Israel Journal of Mathematics. Volume 216, Issue 2, pp. 973-1022, 2016.


23. Philipp Lücke and Philipp Schlicht. Continuous images of closed sets in generalized Baire spaces.
    Israel Journal of Mathematics. Volume 209, Issue 1, pp. 421-461, 2015.


24. Sy David Friedman, Peter Holy and Philipp Lücke. Large cardinals and lightface definable well-orders, without the GCH.
    Journal of Symbolic Logic. Volume 80, Issue 1, pp. 251-284, 2015.


25. David Asperó, Peter Holy and Philipp Lücke. Forcing lightface definable well-orders, without the GCH.
    Annals of Pure and Applied Logic. Volume 166, Issue 5, pp. 553-582, 2015.


26. Sy David Friedman and Philipp Lücke. Large cardinals and definable well-orders, without the GCH.
    Annals of Pure and Applied Logic. Volume 166, Issue 3, pp. 306-324, 2015.


27. Philipp Lücke and Saharon Shelah. Free groups and automorphism groups of infinite structures.
    Forum of Mathematics, Sigma. Volume 2, 18 pages, 2014.


28. Peter Holy and Philipp Lücke. Locally Σ₁-definable well-orders of H(κ⁺).
    Fundamenta Mathematicae. Volume 226, Issue 3, pp. 221-236, 2014.


29. Philipp Lücke. Σ¹₁-definability at uncountable regular cardinals.
    Journal of Symbolic Logic. Volume 77, Issue 3, pp. 1011-1046, 2012.


30. Philipp Lücke. Special pairs and automorphisms of centreless groups.
    In Groups and Model Theory, Contemporary Mathematics. Volume 576, pp. 239-254, 2012.


31. Philipp Lücke. Groups with unbounded potential automorphism tower heights.
    In Future directions for logic. Proceedings of PhDs in Logic III, IfColog Proceedings. Volume 2, pp. 81-90, 2012.


32. Gunter Fuchs and Philipp Lücke. Iteratively changing the heights of automorphism towers.
    Notre Dame Journal of Formal Logic. Volume 53, Issue 2, pp. 155-174, 2012.


33. Philipp Lücke and Saharon Shelah. External automorphisms of ultraproducts of finite models.
    Archive for Mathematical Logic, Volume 51, Issue 3, pp. 433-441, 2012.


34. Philipp Lücke and Simon Thomas. Automorphism groups of ultraproducts of finite symmetric groups.
    Communications in Algebra. Volume 39, Issue 10, pp. 3625-3630, 2011.

Theses

• Philipp Lücke. Complexity, definability and descriptive methods at higher cardinals.
  Habilitation thesis. Rheinische Friedrich-Wilhelms-Universität Bonn, 2018.


• Philipp Lücke. Automorphism towers and definability in generalized Baire spaces.
  Dissertation. Westfälische Wilhelms-Universität Münster, 2012.

Extended abstracts

• Philipp Lücke. Simple formulas defining complicated sets.
Proceedings in Applied Mathematics and Mechanics. Volume 16, Issue 1, pp. 907-908, 2016.