Publications
(with Marlene Koelbing, Philipp Schlicht and Wolfgang Wohofsky) The Edinburgh topology on generalized Baire spaces.
In preparation. talk slides 1 talk slides 2 talk slides 3 talk slides 4
(with Brent Cody) Large Cardinal Operators and Higher Indescribability.
Submitted, 2021. pdf
Large Cardinal Operators and Elementary Embeddings.
Submitted, 2020. pdf talk slides
(with Philipp Lücke) Small Models, Large Cardinals, and Induced Ideals.
Annals of Pure and Applied Logic 172, no. 2, 50 pages, 2021. pdf talk slides 1 talk slides 2
(with Philipp Lücke and Ana Njegomir) Characterizing Large Cardinals through Neeman's pure side condition forcing.
Fundamenta Mathematicae 252, pp. 53-102, 2021. pdf talk slides
(with Victoria Gitman, Joel Hamkins, Philipp Schlicht and Kameryn Williams) The exact Strength of the Class Forcing Theorem.
Journal of Symbolic Logic 85, no. 3, pp. 869-905, 2020. 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
Unpublished Notes
(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
Past Talks
Large Cardinals
Ramsey-like Operators
Torino/Udine logic seminar, 20.11.2020; Set Theory in the UK workshop, 04.12.2020; Kurt Gödel Research Center, 17.12.2020 --> pdf
Uniform Large Cardinal Characterisations and Ideals up to measurability
New York Set Theory Seminar, 10.07.2020 --> pdf
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
Generalized or Higher Descriptive Set Theory
Ideal Topologies
Bristol Logic and Set Theory Seminar, 10.06.2020 --> pdf
Generalised Topologies on 2^kappa, Silver forcing and Diamond
Udine Logic Seminar, 29.05.2020 --> pdf
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)
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.
----------------------------------------
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.
Update log here.