(with Marlene Koelbing, Philipp Schlicht and Wolfgang Wohofsky) The Edinburgh topology on generalized Baire spaces.
In preparation. talk slides 1 talk slides 2

(with Philipp Lücke) Small Models, Large Cardinals, and Induced Ideals.
Submitted, 2019. pdf talk slides

(with Philipp Lücke and Ana Njegomir) Characterizing Large Cardinals through Neeman's pure side condition forcing.
Accepted for Fundamenta Mathematicae, 2020. pdf talk slides

(with Victoria Gitman, Joel Hamkins, Philipp Schlicht and Kameryn Williams) The exact Strength of the Class Forcing Theorem.
Accepted for the Journal of Symbolic Logic, 2019. pdf talk slides

(with Philipp Lücke and Ana Njegomir) Small Embedding Characterizations for Large Cardinals.
Annals of Pure and Applied Logic 170, no. 2, pp. 251-271, 2019. pdf talk slides

(with Regula Krapf and Philipp Schlicht) Sufficient conditions for the forcing theorem, and turning proper classes into sets.
Fundamenta Mathematicae 246, pp 27-44, 2019. pdf

(with Philipp Schlicht) A Hierarchy of Ramsey-like cardinals.
Fundamenta Mathematicae 242, pp 49-74, 2018. pdf

(with Regula Krapf and Philipp Schlicht) Characterizations of Pretameness and the Ord-cc.
Annals of Pure and Applied Logic 169, no. 8, pp. 775-802, 2018. pdf

(with Philipp Lücke) Simplest possible locally definable Wellorders.
Fundamenta Mathematicae 236, pp. 101-139, 2017. pdf talk slides

(with Regula Krapf, Philipp Lücke, Ana Njegomir and Philipp Schlicht) Class Forcing, the Forcing Theorem and Boolean Completions.
Journal of Symbolic Logic 81, no. 4, pp. 1500-1530, 2016. pdf talk slides

Sigma_1-Wellorders without Collapsing.
Archive for Mathematical Logic 54, issue 3, pp 453-462, 2015. pdf talk slides

(with David Asperó and Philipp Lücke) Forcing lightface Definable Wellorders without the GCH.
Annals of Pure and Applied Logic 166, no. 5, pp. 553-582, 2015. pdf, David Asperó's talk slides

(with Philip Welch and Liuzhen Wu) Local Club Condensation and L-likeness.
Journal of Symbolic Logic 80, no. 4, pp. 1361-1378, 2015. pdf, talk slides

(with Sy-David Friedman and Philipp Lücke) Large Cardinals and Lightface Definable Wellorders without GCH.
Journal of Symbolic Logic 80, issue 1, pp 251-284, 2015. pdf, talk slides

(with Philipp Lücke) Locally Sigma_1-definable Wellorders of H(kappa^+).
Fundamenta Mathematicae 226, pp 221-236, 2014. pdf, talk slides

(with Sy-David Friedman) A Quasi Lower Bound on the Consistency Strength of PFA.
Transactions of the AMS 366, pp 4021-4065, 2014. pdf, talk slides

(with Sy-David Friedman) Condensation and Large Cardinals.
Fundamenta Mathematicae 215, no. 2, pp 133-166, 2011. pdf, info

Dissertation: Condensation and Large Cardinals.
(2010, advisor: Sy D. Friedman) pdf, info

Masters Thesis: Absoluteness Results in Set Theory.
(2007, advisor: Sy D. Friedman) pdf

(with Philipp Lücke) A countable support iteration for the tree property at aleph_2 and related properties.
(2020) pdf

A short forcing argument for the proper forcing axiom using Magidor's characterization of supercompactness.
(2019) pdf

(with Regula Krapf and Philipp Schlicht) Separation in Class Forcing Extensions.
(2017) pdf

A generalization of the notion of bounded degree for infinite graphs.
(2014) pdf

PFA and Class Forcing.
(2013) pdf

Canonical Function Coding over a Stationary Set.
(2013) pdf, info

Condensation and Large Cardinals - A Simplified Version of my Dissertation.
(2013) pdf, info

Ideal Topologies
Udine Logic Seminar, 01.04.2020 --> pdf

The Edinburgh Topology
Amsterdam Academy Colloquium on Generalised Baire Spaces, 24.08.2018 (Part I of a two-part talk, part II by Wolfgang Wohofsky) --> pdf

General Audience Talks

Mathematische Unentscheidbarkeit (Undecidability in Mathematics)
Antrittsvorlesung, Dies Academicus, University of Bonn, 04.12.2019 --> pdf (in German)

Large Cardinals

Small Models, Large Cardinals, and Large Cardinal Ideals
Bonn Logic Seminar, 23.10.2018; European Set Theory Conference, Vienna, 05.07.2019 --> pdf

Characterizing Large Cardinals through Forcing
Set Theory Today Conference, Vienna, 10.09.2018 --> pdf

A Hierarchy of Ramsey-like cardinals
Bristol Set Theory Seminar, 07.03.2017

Small embedding characterizations for large cardinals, and internal large cardinals
Bonn Logic Seminar, 09.05.2016; Young Set Theory Workshop, Copenhagen, 16.06.2016; Kurt Gödel Research Center, 06.04.2017 --> pdf

General Mathematics Audience Talks

A surprising equality between two infinities (p=t)
Habilitation Colloquium, Bonn, 31.01.2019

Surreal Numbers
Basic Notions Seminar, Bonn, 25.10.2016 (following slides by Yurii Khomskii)

Forcing: How to prove Unprovability
Basic Notions Seminar, Bonn, 18.11.2015 (Part II of a two-part talk, part I by Regula Krapf).

The Outer Model Programme
Norwich Pure Maths Seminar, 28.04.2014 --> pdf

Class Forcing

The exact Strength of the Class Forcing Theorem
Bonn Logic Seminar, 23.10.2017 --> pdf

How to and how not to turn proper classes into sets
Bonn Logic Seminar, 24.10.2016

Class Forcing and Pretameness
Hamburg Logic Seminar, 30.05.2016

Failures of the Forcing Theorem
European Set Theory Conference, Cambridge, 25.08.2015 --> pdf

Non-pretame Class Forcing and the Forcing Theorem, the axioms of ZFC and non-definable Class Forcing
Kurt Gödel Research Center, Vienna, 27.05.2015

The Dark Side of Class Forcing
Bristol Logic Seminar, 10.03.2015

Locally Definable Wellorders

Forcing lightface definable Wellorders without the GCH
Bonn Logic Seminar, 09.11.2015

Delta^1_1 subsets of the generalized Baire Space
Amsterdam workshop on Set Theory, 03.11.2014 --> pdf

Simplest Possible Wellorders of H(kappa^+)
Winter School in Abstract Analysis, section Set Theory and Topology, Hejnice, 26.01.2014; Bonn Logic Seminar, 19.02.2014; Bristol Logic Seminar, 18.03.2014

Locally Sigma_1-definable wellorders of H(kappa^+)
ESI Workshop on Forcing and Large Cardinals, Vienna, 23.09.2013

Large Cardinals and lightface definable Wellorders without the GCH
Kurt Gödel Research Center, Vienna, 10.01.2013; Bristol Logic Seminar, 11.03.2013 --> pdf

Condensation and the Outer Model Programme

Condensation does not imply Square
Inner and Outer Model Theory Workshop, Bristol, 06.07.2014; Bonn Logic Seminar, 20.04.2015; Münster Set Theory Seminar, 11.06.2015; Logic Colloquium, Helskinki, 03.08.2015 --> pdf

The Outer Model Programme
Oxford Logic Seminar, 07.02.2013 --> pdf

L-like Models with Large Cardinals and a quasi lower Bound on the Consistency Strength of PFA.
PhD Colloquium Paderborn, 13.09.2012; Bristol Logic Seminar, 28.11.2012; Bonn Logic Seminar, 08.04.2013; Young Set Theory Workshop Oropa, 12.07.2013 --> pdf

Teaching

Current Teaching

None.

Past Teaching

at the University of Bonn:

autumn 2019: Models of Set Theory 2 -- Iterated forcing and its applications (lecture and exercises)

spring 2019:
Exercises for Basic Features of Mathematics II
Seminar in Set Theory -- Large Cardinals (with Peter Koepke)

autumn 2018:
Exercises for Basic Features of Mathematics I

spring 2018:
Exercises for Basic Features of Mathematics II
Seminar in Logic -- Large Cardinals and Strong Logics

autumn 2017:
Exercises for Basic Features of Mathematics I
Seminar in Set Theory -- Constructibility (with Peter Koepke, Philipp Lücke and Philipp Schlicht)

spring 2017: Exercises for Models of Set Theory

autumn 2015: Exercises for Elements of Mathematics

spring 2015:
Seminar in Logic -- Constructibility (with Peter Koepke)
Exercises for Introduction to Mathematical Logic
Logic Bachelor thesis seminar (with Peter Koepke and Philipp Lücke)

autumn 2014: Exercises for Elements of Mathematics

at the University of Bristol:

2013/2014: Mathematics Tutorials for 1st year students (Analysis, Group Theory, Number Theory)
2012/2013: Mathematics Tutorials for 1st year students (Analysis, Group Theory, Number Theory)

at the Kurt Gödel Research Center for Mathematical Logic, Vienna:

autumn 2011:
Reading Course in Set Theory
Exercises for Introduction to Mathematical Logic.

spring 2011: Exercises for Axiomatic Set Theory 1.
spring 2010: Exercises for Axiomatic Set Theory 1.
spring 2009: Exercises for Axiomatic Set Theory 1.
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Old Exercises (Models of Set Theory 2, autumn 2019): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
Old Exercises (Elements of Mathematics, autumn 2015): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.
Old Exercises (Introduction to Mathematical Logic, spring 2015): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Old Exercises (Introduction to Mathematical Logic, autumn 2011): 1, 2, 3, 4, 5, 6, 7, 8, 9.
Reading Course in Set Theory info.
Old Exercises (Axiomatic Set Theory 1, spring 2011): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Old Exercises (Axiomatic Set Theory 1, spring 2010): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
Old Exercises (Axiomatic Set Theory 1, spring 2009): 1, 2, 3, 4, 5, 6, 7, 8.