Stefan Hoffelner

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5 papers · 1 filter

math.LO2025

$MA (I$ ) and a Failure of Separation on the third Level

Stefan Hoffelner

We present a method which forces the failure of $Π_{3}^{1}$ and $Σ_{3}^{1}$ -separation, while $MA (I$ ) holds, for $I$ the family of indestructible ccc forcings…

math.LO2025

$NS_{ω_{1}}$ saturated, $Δ_{1} ({ω_{1}})$ -definable and a $Δ_{4}^{1}$ -definable well-order of the reals

Stefan Hoffelner

Assuming $M_{1}$ , the canonical inner model with one Woodin cardinal exists, we construct a model in which the nonstationary ideal on $ω_{1}$ is $ℵ_{2}$ -saturated, $Δ_{1}$ -definable w…

math.LO2025

A Universe with a $Δ_{n}^{1}$ -definable well-order of the reals, $CH$ and $Π_{n}^{1}$ -Uniformization

Stefan Hoffelner

This paper details the construction of a universe where $Π_{3}^{1}$ -uniformization is true, the Continuum Hypothesis holds yet it possesses a $Δ_{3}^{1}$ -definable well-order of its reals.…

math.LO2025

A Universe with large Continuum, global $Σ$ -Uniformization and a projective Well-Order of its Reals

Stefan Hoffelner

We construct a model in which the continuum has size $κ$ for a regular cardinal $κ$ and in which the $Σ_{n}^{1}$ -uniformization property holds simultaneously for every $n \geq 2$ . Addit…

math.LO2017

A universe with no ordinal-definable, stationary, co-stationary subset of $ω_{1}$

Stefan Hoffelner

It is shown that the existence of a measurable cardinal is equiconsistent to a model of ZFC in which there is no ordinal-definable, stationary, costationary subset of $ω_{1}$

MA(I) and a Failure of Separation on the third Level

NSω1​​ saturated, Δ1​({ω1​})-definable and a Δ41​-definable well-order of the reals

A Universe with a Δn1​-definable well-order of the reals, CH and Πn1​-Uniformization

A Universe with large Continuum, global Σ-Uniformization and a projective Well-Order of its Reals

A universe with no ordinal-definable, stationary, co-stationary subset of ω1​

$MA (I$ ) and a Failure of Separation on the third Level

$NS_{ω_{1}}$ saturated, $Δ_{1} ({ω_{1}})$ -definable and a $Δ_{4}^{1}$ -definable well-order of the reals

A Universe with a $Δ_{n}^{1}$ -definable well-order of the reals, $CH$ and $Π_{n}^{1}$ -Uniformization

A Universe with large Continuum, global $Σ$ -Uniformization and a projective Well-Order of its Reals

A universe with no ordinal-definable, stationary, co-stationary subset of $ω_{1}$