Stefan Hoffelner

Set theory, forcing, descriptive set theory, and inner model theory.

I received my PhD from the Kurt Gödel Research Center in Vienna in 2016 under the supervision of S. D. Friedman. I was a postdoctoral researcher at Charles University Prague in 2017, working with J. Verner. From 2018 to 2024 I was an Assistant Professor at the University of Münster, working in R. D. Schindler’s group, and I obtained my Habilitation there in 2025.

I am a project leader and senior postdoc in the Set Theory group at TU Wien, where I lead the FWF Einzelprojekt P 37228, Investigating separation, reduction and uniformization, 2024–2028. My research concerns definability and forcing, with a focus on separation, reduction and uniformization principles for projective sets of reals, definable well-orders, forcing axioms, and canonical inner models with Woodin cardinals.

Publications · Research · CV

Contact

TU Wien

Research Unit Set Theory

Institute of Discrete Mathematics and Geometry

Email: stefan.hoffelner@tuwien.ac.at

Selected works

• The global (\Sigma^1_{n+2})-Uniformization Property and BPFA.
  This paper shows that global projective uniformization can be forced together with BPFA, separating uniformization from the classical route through good projective wellorders.
  DOI

• Forcing the (\Sigma^1_3)-separation property.
  This paper gives an early forcing construction in which projective separation phenomena are isolated at the (\Sigma^1_3) level.
  DOI

• Forcing the (\Pi^1_3)-Reduction Property and a Failure of (\Pi^1_3)-Uniformization.
  This paper separates projective reduction from projective uniformization by producing a model where (\Pi^1_3)-reduction holds but (\Pi^1_3)-uniformization fails.
  DOI

• Local forms of Woodin’s 12th Delfino problem, including joint work with Sandra Müller.
  These companion papers prove finite-level local versions of Woodin’s 12th Delfino problem, with complementary (\Pi)-side and (\Sigma)-side constructions.
  (\Pi)-side arXiv · (\Pi)-side PDF
  (\Sigma)-side arXiv · (\Sigma)-side PDF

• PFA and the definability of the nonstationary ideal, with P. Larson, R. Schindler and L. Wu.
  This paper studies how forcing axioms interact with definability questions around the nonstationary ideal.
  DOI

See the full publications list.