Stefan Hoffelner's Webpage

Stefan Hoffelner

I am a Mathematician working in Set Theory. Currently I am holding a position at the TU Vienna which is funded by the Austrian Science Fund (FWF), Project P 37228-N. Before that I was an Assistant at the University of Münster where I was part of the Institut für Mathematische Logik und Grundlagenforschung, working in R. D. Schindler's group. I did my PhD under the supervision of S. D. Friedman at the Kurt Gödel Research Center in Vienna.

Publications and Preprints

Some of my mathematical work can be found below.

The global $\Sigma^1_{n+1}$-Uniformization and $\mathsf{BPFA}$ Submitted

A Failure of $\Pi^1_{n+3}$-Reduction in the Presence of $\Sigma^1_{n+3}$-Separation Submitted

PFA and the definability of the non-stationary ideal. Joint with P. Larson, R. D. Schindler and L. Wu. Submitted
Forcing Axioms and the Definability of the Nonstationary Ideal on $\omega_1$. Joint with P. Larson, R. D. Schindler and L. Wu. Accepted at the Journal of Symbolic Logic.
Forcing the $\Pi^1_n$-Uniformization property. Submitted.
Forcing the $\Pi^1_3$-Reduction property and a failure of $\Pi^1_3$-Uniformization. Annals of Pure and Applied Logic 2023.
Forcing the $\Sigma^1_3$-Separation Property. Journal of Mathematical Logic (2) 2022. This version uses a slighly altered coding method which makes several proofs and definitions easier.
Forcing Axioms and the Uniformization Property Submitted.
$\hbox{NS}_{\omega_1}$ saturated and $\Delta_1$-definable. Journal of Symbolic Logic (1) 2021.
A $\Sigma^1_4$-definable wellorder of the reals with $\hbox{NS}_{\omega_1}$ saturated. Joint with S. D. Friedman Journal of Symbolic Logic 2019.
My PhD Thesis, written under the supervision of S. D. Friedman at the Kurt Gödel Research Center.
A model with no ordinal-definable stationary, costationary subset of $\omega_1$ Preprint.