- 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.

- Omer Ben-Neria and Philipp Lücke.
**On Σ**._{1}-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.

- 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. - Philipp Lücke and Sandra Müller.
**Σ**._{1}-definability at higher cardinals: Thin sets, almost disjoint families and long well-orders

*Forum of Mathematics, Sigma*. Volume 11, 36 pages, 2023. - Philipp Lücke and Ioannis Souldatos.
**Non-absoluteness of Hjorth's cardinal characterization**.

*Fundamenta Mathematicae*. Volume 262, Issue 2, pp. 105-128, 2023. - Joan Bagaria and Philipp Lücke.
**Huge reflection**.

*Annals of Pure and Applied Logic*. Volume 174, Issue 1, 32 pages, 2023. - 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. - Philipp Lücke.
**Structural reflection, shrewd cardinals and the size of the continuum**.

*Journal of Mathematical Logic*. Volume 22, Issue 2, 43 pages, 2022. - Philipp Lücke.
**Strong unfoldability, shrewdness and combinatorial consequences**.

*Proceedings of the American Mathematical Society*. Volume 150, Issue 9, pp. 4005-4020, 2022. - Philipp Lücke and Sandra Müller.
**Closure properties of measurable ultrapowers**.

*Journal of Symbolic Logic*. Volume 86, Issue 2, pp. 762-784, 2021. - 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. - 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. - Philipp Lücke.
**Partition properties for simply definable colourings**.

*Israel Journal of Mathematics*. Volume 236, Issue 2, pp. 841-898, 2020. - Philipp Lücke.
**Closed maximality principles and generalized Baire spaces**.

*Notre Dame Journal of Formal Logic*. Volume 60, Number 2, pp. 253-282, 2019. - 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. - Chris Lambie-Hanson and Philipp Lücke.
**Squares, ascent paths, and chain conditions**.

*Journal of Symbolic Logic*. Volume 83, Issue 4, pp. 1512-1538, 2018. - Philipp Lücke and Philipp Schlicht.
**Measurable cardinals and good Σ**._{1}(κ)-wellorderings

*Mathematical Logic Quarterly*. Volume 64, Issue 3, pp. 207-217, 2018. - Philipp Lücke, Philipp Schlicht and Thilo Weinert.
**Choiceless Ramsey theory of linear orders**.

*Order*. Volume 34, Issue 3, pp. 369-418, 2017. - Philipp Lücke, Ralf Schindler and Philipp Schlicht.
**Σ**._{1}(κ)-definable subsets of H(κ^{+})

*Journal of Symbolic Logic*. Volume 82, Issue 3, pp. 1106-1131, 2017. - Philipp Lücke.
**Ascending paths and forcings that specialize higher Aronszajn trees**.

*Fundamenta Mathematicae*. Volume 239, Issue 1, pp. 51-84, 2017. - 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. - Peter Holy and Philipp Lücke.
**Simplest possible locally definable well-orders**.

*Fundamenta Mathematicae*. Volume 236, Issue 2, pp. 101-139, 2017. -
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. - 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. - 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. - 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. - 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. - 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. - Philipp Lücke and Saharon Shelah.
**Free groups and automorphism groups of infinite structures**.

*Forum of Mathematics, Sigma*. Volume 2, 18 pages, 2014. - Peter Holy and Philipp Lücke.
**Locally Σ**._{1}-definable well-orders of H(κ^{+})

*Fundamenta Mathematicae*. Volume 226, Issue 3, pp. 221-236, 2014. - Philipp Lücke.
**Σ**.^{1}_{1}-definability at uncountable regular cardinals

*Journal of Symbolic Logic*. Volume 77, Issue 3, pp. 1011-1046, 2012. - Philipp Lücke.
**Special pairs and automorphisms of centreless groups**.

In*Groups and Model Theory*, Contemporary Mathematics. Volume 576, pp. 239-254, 2012. - 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. - 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. - Philipp Lücke and Saharon Shelah.
**External automorphisms of ultraproducts of finite models**.

*Archive for Mathematical Logic*, Volume 51, Issue 3, pp. 433-441, 2012. - Philipp Lücke and Simon Thomas.
**Automorphism groups of ultraproducts of finite symmetric groups**.

*Communications in Algebra*. Volume 39, Issue 10, pp. 3625-3630, 2011.

- 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.

- Philipp Lücke.
**Simple formulas defining complicated sets**.