Philipp Schlicht Mathematics

Research


My research field is mathematical logic, in particular set theory, large cardinals, descriptive set theory and applications to analysis, model theory, graph theory, computability and theoretical computer science.

I work on the EPSRC project ‘‘Graphs on generalised Baire spaces’’ with Prof. Philip Welch at the University of Bristol. In which circumstances can you colour a graph with few colours such that no adjacent vertices are assigned the same colour? We study this problem in the context of graphs of a specified complexity such as open, closed or Borel as a subset of the plane. The study of such graphs led Todorcevic to devise the open colouring axiom. We aim to understand graphs and hypergraphs of finite and infinite dimension on large spaces. These spaces appear naturally in set theory and model theory.

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Selected publications

Submitted papers
  1. The open dihypergraph dichotomy on generalized Baire spaces and its applications
    with Dorottya Sziraki, 107 pages, preprint on arxiv.org
  2. Forcing over choiceless models and generic absoluteness
    with Daisuke Ikegami, 28 pages, submitted
  3. Countable ranks at the first and second projective levels
    with Merlin Carl and Philip Welch, 30 pages, submitted
  4. Generalized Polish spaces at regular uncountable cardinals
    with Claudio Agostini and Luca Motto Ros, 42 pages, submitted

Selected papers by venue or impact
  1. Coarse groups, and the isomorphism problem for oligomorphic groups
    with Andre Nies and Katrin Tent, Journal of Mathematical Logic 22, 1 (2022), 2150029, 26 pages
  2. Lebesgue's density theorem and definable selectors for ideals
    with Sandra Müller, David Schrittesser and Thilo Weinert, Israel Journal of Mathematics 249 (2022), 501–551
  3. 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), 1-12
  4. The exact strength of the class forcing theorem
    with Victoria Gitman, Joel David Hamkins, Peter Holy and Kameryn Williams, Journal of Symbolic Logic, Volume 85, Issue 3 (2020), 869-905
  5. Perfect subsets of generalized Baire spaces and long games
    Journal of Symbolic Logic 82, 4 (2017),1317-1355
  6. The Hurewicz dichotomy for generalized Baire spaces
    with Luca Motto Ros and Philipp Lücke, Israel Journal of Mathematics 216, 2 (2016), 973-1022
  7. 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

Updates

Asymmetric cut and choose games accepted for Bulletin of Symbolic Logic - February 2, 2023