A. Lietz

collaborators

5 papers

math.LO2025

Separating Maximality Principles

Takehiko Gappo, Andreas Lietz

We investigate fragments of generic absoluteness principles known as Maximality Principles. We determine the consistency strength of $Σ_{n}$ - $MP (R)$ and $Π_{n}$ -$\math…

math.LO2024

Infinite Hat Problems and Large Cardinals

Andreas Lietz, Jeroen Winkel

Picture countably many logicians all wearing a hat in one of $κ$ -many colours. They each get to look at finitely many other hats and afterwards make finitely many guesses for their…

math.LO2024

Forcing " $NS_{ω_{1}}$ is $ω_{1}$ -dense" From Large Cardinals

Andreas Lietz

We answer a question of Woodin by showing that assuming an inaccessible cardinal $κ$ which is a limit of $< κ$ -supercompact cardinals exists, there is a stationary set preserving…

math.LO2024

An Iteration Theorem for $ω_{1}$ -preserving Forcings

Andreas Lietz

We prove an iteration theorem which guarantees for a wide class of nice iterations of $ω_{1}$ -preserving forcings that $ω_{1}$ is not collapse, at the price of needing large cardinals…

math.LO2024

The Axiom of Choice in the $κ$ -Mantle

Andreas Lietz

Usuba has asked whether the $κ$ -mantle, the intersection of all grounds that extend to $V$ via a forcing of size $< κ$ , is always a model of ZFC. We give a negative answers by con…

Separating Maximality Principles

Infinite Hat Problems and Large Cardinals

Forcing "NSω1​​ is ω1​-dense" From Large Cardinals

An Iteration Theorem for ω1​-preserving Forcings

The Axiom of Choice in the κ-Mantle

Forcing " $NS_{ω_{1}}$ is $ω_{1}$ -dense" From Large Cardinals

An Iteration Theorem for $ω_{1}$ -preserving Forcings

The Axiom of Choice in the $κ$ -Mantle