About me

I am a Heisenberg fellow and Privatdozent at the University of Hamburg, where I am a member of the research group Mathematical Logic and Interdisciplinary Applications of Logic at the Department of Mathematics.

My fields of research are Mathematical Logic and Set Theory. My research focuses on the theory of large cardinals, infinitary combinatorics, set-theoretic definability and applications of set theory in algebra.

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Recent activities

• Member of the Editorial Board of Mathematical Logic Quarterly.
• Organizers of the Section “Mathematical Logic” at the DMV Meeting 2023.
• Minisymposium on “Large cardinals” at the Joint Annual Conference of the German Mathematical Society and the Austrian Mathematical Society (28.-30. September 2021).

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Selected Publications

• (with Joan Bagaria) Patterns of Structural Reflection in the large-cardinal hierarchy.
  Transactions of the American Mathematical Society, Volume 377, Issue 5, 3397-3447, 2024.
• (with Sandra Müller) Σ₁-definability at higher cardinals: Thin sets, almost disjoint families and long well-orders.
  Forum of Mathematics, Sigma, Volume 11, 36 pp., 2023.
• Structural reflection, shrewd cardinals and the size of the continuum.
  Journal of Mathematical Logic, Volume 22, Issue 2, 43 pp., 2022.
• Partition properties for simply definable colourings.
  Israel Journal of Mathematics, Volume 236, Issue 2, pp. 841-898, 2020.
• (with Saharon Shelah) Free groups and automorphism groups of infinite structures.
  Forum of Mathematics, Sigma, Volume 2, 18 pp., 2014.

Complete list of publications

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Recent Preprints

• The complexity of non-stationary ideals.
• (with Peter Holy and Sandra Müller) Outward compactness.
• (with Vincenzo Dimonte and Martina Iannella) Descriptive properties of I2-embeddings.
• (with Omer Ben-Neria) On Σ₁-definable closed unbounded sets.

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Current Teaching

• Seminar: Measure and Category (Hamburg, Summer 24).
• Seminar: Combinatorial Set Theory (Hamburg, Winter 23/24).

• All teaching activities

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Recent Talks

• Separating rank-into-rank axioms through their descriptive consequences. Generalised Baire Space and Large Cardinals. Bristol, 08. February 2024.
• Perfect Set Theorems at singular cardinals. RIMS Set Theory Workshop 2023. Kobe, 27. October 2023.
• Weak compactness cardinals for strong logics. XVII International Luminy Workshop in Set Theory . Marseille, 13. October 2023.
• Definable clubs. Set Theory Seminar. Kobe, 31. July 2023.

• More talks

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Funded research projects

• Heisenberg Project: Definability and singular cardinals
• MSCA Project: Strong Axioms of Infinity - Frameworks, Interactions and Applications
• DFG-Project: Complexity and Definability at Higher Cardinals - Studies in Generalized Descriptive Set Theory (LU2020/1-1).

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Supervision

Ana Njegomir (PhD Thesis: Small embeddings, forcing with side conditions, and large cardinal characterizations. Bonn, 2019).

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Profiles

• MathSciNet
• Orchid
• Google Scholar

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Contact Information