Philipp Lücke

Philipp Lücke is a Heisenberg Fellow and Privatdozent at the Department of Mathematics, University of Hamburg, where he conducts research in mathematical logic and set theory. He is a member of the research group Mathematical Logic and Interdisciplinary Applications of Logic.

Research Interests: His work centers on advanced topics in set theory, including large cardinals, infinitary combinatorics, definability at higher cardinals, and structural reflection. He investigates interactions between strong axioms of infinity, forcing, inner model theory, and descriptive set-theoretic methods in generalized Baire spaces.

The most recent publications reflect a consistent focus on the interplay between definability, reflection principles, and large cardinal axioms. Key trends include the analysis of structural reflection across the large cardinal hierarchy, Σ₁-definability at uncountable cardinals, and the behavior of ideals and clubs under forcing extensions. His work often connects model-theoretic and combinatorial properties with foundational questions in set theory.

Scientific Awards and Recognition:

• Heisenberg Fellowship from the German Research Foundation (DFG)
• Member of the Editorial Board of Zeitschrift für Mathematische Logik und Grundlagen der Mathematik

Supervision and Grants: Lücke supervises doctoral students, including Dr. Ana Njegomir. He leads multiple funded research projects, such as the DFG project Complexity and Definability at Higher Cardinals (LU2020/1-1), the Heisenberg Project Definability and Singular Cardinals, and the MSCA project Strong Axioms of Infinity - Frameworks, Interactions and Applications (SAIFIA). These projects highlight his role as an independent principal investigator in foundational mathematics.

Laboratories and Research Groups: He is an active member of the Mathematical Logic and Interdisciplinary Applications of Logic research group at the University of Hamburg, contributing to seminars, workshops, and collaborative research in set theory and logic.