Algebra Seminar talk
2026-04-24
Stefan Hoffelner
Models where all $\boldsymbol{\Sigma}^1_{n+2}$-sets are Lebesgue measurable and have the Baire property in the presence of global $\Sigma_{n+3+m}$-uniformization and a $\Delta^1_{n+3}$-definable wellorder of the reals
Abstract:
Assuming that $M_n$, the canonical inner model with $n$-many Woodin cardinals exists, we force a model where every $\boldsymbol{\Sigma}^1_{n+2}$ set is Lebesgue measurable, has the Baire property and the $\Sigma^1_{n+3+m}$-uniformization property holds for every $m \in \omega$. Additionally this universe has a $\Delta^1_{n+3}$-definable wellorder of the reals. I will present and highlight the main ideas and intuitions which drive the construction of the desired universe. This is joint work with S. Mueller.