Stefan Hoffelner

activity

20162026

Σ_{3}^{1}

-Separation Property

5 citations · 13 across the 22 of their papers we have counts for

collaborators

22 papers

math.LO2026

On a local variant of the 12th Delfino problem -- the $Π$ -side

Stefan Hoffelner

Assume that $M_n$, the canonical inner model with $n$ Woodin cardinals, exists. We force a model with continuum $\aleph_2$ in which every $\boldsymbolΣ^1_{n+2}$ set of real…

math.LO2026

On a local variant of the 12th Delfino problem -- the $Σ$ -side

Stefan Hoffelner, Sandra Müller

Assuming that $M_{n}$ , the canonical inner model with $n$ Woodin cardinals, exists, we force a model in which every $Σ_{n + 2}^{1}$ set is Lebesgue measurable and has the Bair…

math.LO2026

Martin's Axiom, Large Continuum and Global $Σ_{n}^{1}$ -Uniformization

Stefan Hoffelner

We construct a generic extension of $L$ satisfying Martin's Axiom, $2^{ℵ_{0}} = ℵ_{3}$ , a lightface $Δ_{3}^{1}$ wellorder of the reals, and $Σ_{n}^{1}$ -uniformization for every $n\geq…

math.LO2026

On graphs of total projective functions

Stefan Hoffelner

It is well known that the graph of a total $Σ_{n}^{1}$ -function is $Π_{n}^{1}$ . We prove the consistency of the dual assertion at the third projective level: there is a model…

math.LO2026

Forcing $Σ_{1}^{1}$ -Separation on $ω_{1}^{ω_{1}}$

Stefan Hoffelner

We prove that it is consistent that every two disjoint boldface $Σ_{1}^{1}$ subsets of $ω_{1}^{ω_{1}}$ can be separated by a boldface $Δ_{1}^{1}$ set. The forcing starts from $L$ …

math.LO2026

On $Σ_{3}^{1}$ - and $Σ_{4}^{1}$ -uniformization

Stefan Hoffelner

Assuming the consistency of $ZFC$ , we construct a model of set theory in which the boldface $Σ_{3}^{1}$ -uniformization property holds, yet the lightface $Σ_{4}^{1}$ -uniform…

math.LO2025

Forcing upper $Σ$ -uniformization in the presence of lower $Π$ -reduction or uniformization

Stefan Hoffelner

We present a method which allows the combination of forcing uniformization on the $Π$ - and the $Σ$ -side of the projective hierarchy to a certain extent. Using this method we constr…

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.LO2024

The global $Σ_{n + 1}^{1}$ -Uniformization Property and $BPFA$

Stefan Hoffelner

We show that given a reflecting cardinal, one can produce a model of $BPFA$ where the $Σ_{n}^{1}$ -uniformization property holds simultaneously for all $n \geq 2$ .

math.LO2023

A Failure of $Π_{n + 3}^{1}$ -Reduction in the Presence of $Σ_{n + 3}^{1}$ -Separation

Stefan Hoffelner

We show that one can force over $L$ that $Σ_{3}^{1}$ -separation holds, while $Π_{3}^{1}$ -reduction fails, thus separating these two principles for the first time. The construction can be l…

math.LO2023

PFA and the definability of the nonstationary ideal

Stefan Hoffelner, Paul Larson, Ralf Schindler +1

We produce, relative to a $ZFC$ model with a supercompact cardinal, a $ZFC$ model of the Proper Forcing Axiom in which the nonstationary ideal on $ω_{1}$ is $Π_{1}$ -definab…

math.LO2022★ 2 cited

Forcing Axioms and the Definabilty of the Nonstationary Ideal on $ω_{1}$

Stefan Hoffelner, Paul Larson, Ralf Schindler +1

We show that under $\BMM$ and "there exists a Woodin cardinal $"$ , the nonstationary ideal on $ω_{1}$ can not be defined by a $Σ_{1}$ formula with parameter $A \subset ω_{1}$ . We show tha…

math.LO2021

Forcing the $Π_{n}^{1}$ -Uniformization Property

Stefan Hoffelner

We generically construct a model in which the $Π_{3}^{1}$ -uniformization property is true, thus lowering the best known consistency strength from the existence of $M_{1}^{#}$ to just…

math.LO2020★ 1 cited

Forcing the $Π_{3}^{1}$ -Reduction Property and a Failure of $Π_{3}^{1}$ -Uniformization

Stefan Hoffelner

We force over the constructible universe to obtain a model of the $Π_{3}^{1}$ -reduction property, thus lowering the best known large cardinal strength from the existence of $M_{1}^{#}$ …

math.LO2020★ 2 cited

Forcing Axioms, the Uniformization and the Basis Property

Stefan Hoffelner

We show that there are models of MA where the boldface $Σ_{3}^{1}$ -uniformization property holds. Further we show that BPFA and the assertion $ℵ_{1}$ is accessible to reals outright…

math.LO2019★ 5 cited

The Consistency of the $Σ_{3}^{1}$ -Separation Property

Stefan Hoffelner

We generically construct a model in which the $Σ_{3}^{1}$ -separation property is true, i.e. every pair of disjoint $Σ_{3}^{1}$ -sets can be separated by a $Δ_{3}^{1}$ -definable s…

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 $ω_{1}$

math.LO2017★ 3 cited

NS saturated and $Δ_{1}$ -definable

Stefan Hoffelner

We show that under the assumption of the existence of the canonical inner model with one Woodin cardinal $M_{1}$ , there is a model of $\ZFC$ in which $\NS$ is $ℵ_{2}$ -saturated an…

math.LO2016

Projective Wellorders and the Nonstationary Ideal

Stefan Hoffelner

We show that, under the assumption of the existence of $M_{1}^{#}$ , there exists a model on which the restricted nonstationary ideal $NS ↾ A$ is $ℵ_{2}$ -satu…

On a local variant of the 12th Delfino problem -- the Π-side

On a local variant of the 12th Delfino problem -- the Σ-side

Martin's Axiom, Large Continuum and Global Σn1​-Uniformization

On graphs of total projective functions

Forcing Σ11​-Separation on ω1ω1​​

On Σ31​- and Σ41​-uniformization

Forcing upper Σ-uniformization in the presence of lower Π-reduction or uniformization

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

The global Σn+11​-Uniformization Property and BPFA

A Failure of Πn+31​-Reduction in the Presence of Σn+31​-Separation

PFA and the definability of the nonstationary ideal

Forcing Axioms and the Definabilty of the Nonstationary Ideal on ω1​

Forcing the Πn1​-Uniformization Property

Forcing the Π31​-Reduction Property and a Failure of Π31​-Uniformization

Forcing Axioms, the Uniformization and the Basis Property

The Consistency of the Σ31​-Separation Property

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

NS saturated and Δ1​-definable

Projective Wellorders and the Nonstationary Ideal

On a local variant of the 12th Delfino problem -- the $Π$ -side

On a local variant of the 12th Delfino problem -- the $Σ$ -side

Martin's Axiom, Large Continuum and Global $Σ_{n}^{1}$ -Uniformization

Forcing $Σ_{1}^{1}$ -Separation on $ω_{1}^{ω_{1}}$

On $Σ_{3}^{1}$ - and $Σ_{4}^{1}$ -uniformization

Forcing upper $Σ$ -uniformization in the presence of lower $Π$ -reduction or uniformization

$MA (I$ ) 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

The global $Σ_{n + 1}^{1}$ -Uniformization Property and $BPFA$

A Failure of $Π_{n + 3}^{1}$ -Reduction in the Presence of $Σ_{n + 3}^{1}$ -Separation

Forcing Axioms and the Definabilty of the Nonstationary Ideal on $ω_{1}$

Forcing the $Π_{n}^{1}$ -Uniformization Property

Forcing the $Π_{3}^{1}$ -Reduction Property and a Failure of $Π_{3}^{1}$ -Uniformization

The Consistency of the $Σ_{3}^{1}$ -Separation Property

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

NS saturated and $Δ_{1}$ -definable