Jonathan Schilhan

Currently I am a postdoctoral reasearcher at the University of Leeds. Previously I worked at the University of East Anglia. Before that I have been a doctoral student at the Kurt Gödel Research Center in Vienna.

My research is in set theory. I am mainly working on connections between forcing and combinatorial as well as descriptive set theory.

Mountain View


  1. Preservation of regularity and determinacy in iterations. (with P. Schlicht and J. Schürz) In preparation.
  2. Maximal sets without Choice. submitted.
  3. Sequential and distributive forcings without choice. (with A. Karagila) submitted.
  4. Some combinatorial properties of splitting trees. accepted at Bulletin Polish Acad. Sci. Math.
  5. Tree forcing and definable maximal independent sets in hypergraphs. accepted at the Journal of Symbolic Logic.
  6. Coanalytic ultrafilter bases. Arch. Math. Logic, 61: 567-581, 2022.
  7. Definable towers. (with V. Fischer). Fund. Math., 256: 221-241, 2022.
  8. Towers and gaps at uncountable cardinals. (with V. Fischer, D. C. Montoya and D. Soukup) Fund. Math., 257: 141-166, 2022.
  9. Generalised pseudointersections. Math. Log. Quart., 65: 479-489, 2019.

Talks at Conferences, Seminars, Workshops

  • Logic Colloquium, June 2022, Online - Forcing without AC and DC
  • UEA Maths Research Day, January 2022, invited talk - The Baire property and uniformization.
  • Set Theory in the UK 7, January 2022, invited talk - Sequential and distributive forcing without choice.
  • A Short Talk Series: Research in Set Theory, June 2021, invited talk - Definability of combinatorial sets of reals.
  • RIMS Set Theory Workshop, November 2020, Online Conference - Definability of maximal families of reals in forcing extensions.
  • Toronto Set Theory Seminar, November 2020, Online Seminar - Definable maximal families of reals in forcing extensions.
  • KGRC Research Seminar, October 2020, Online Seminar - Definability of maximal families of reals in forcing extensions.
  • Winter School in Abstract Analysis, January 2020, Hejnice, Czech Republic - The tower spectrum.
  • ÖMG Conference, September 2019, Dornbirn, Austria - The tower spectrum.
  • Winter School in Abstract Analysis, January 2019, Hejnice, Czech Republic - Definability aspects of ultrafilters.
  • Winter School in Abstract Analysis, February 2018, Hejnice, Czech Republic - The generalized meager ideal and clubs.


  • PS Axiomatic Set Theory 1, Summer 2020.


j.[lastname] (at)