Research

My research lies in set theory, forcing, descriptive set theory, and inner model theory.

I am especially interested in forcing constructions which separate regularity, definable choice, reduction, separation, and uniformization phenomena in the projective hierarchy. A recurring theme is the construction of universes of set theory whose reals behave in a controlled and highly regular way, but which lie outside the paradigm of projective determinacy.

Current research themes

• projective uniformization, reduction, and separation;
• definable well-orders of the reals;
• forcing axioms and definability;
• coding methods in forcing;
• canonical inner models with finitely many Woodin cardinals;
• regularity properties of projective sets.

Project

I am the project leader of the FWF Einzelprojekt P 37228, Investigating separation, reduction and uniformization, 2024–2028.