My office is DA05G02, on the fifth floor of the green area in the Freihaus building.
Research Interests: I am working in set theory with a focus on forcing, definability and large cardinals, as well as second order set theory and weak forms of the axiom of choice.
25: (with Jonathan Schilhan) The ordering principle and the axiom of dependent choice. 24: An axiomatic approach to symmetric extensions. 23: (with Philipp Lücke and Sandra Müller) Outward compactness. 22: (with Philipp Schlicht, Christopher Turner and Philip Welch) Asymmetric Cut and Choose Games. 21: (with Brent Cody) Ideal Operators and Higher Indescribability. 20: (with Rodrigo Freire) An ordinal-connection axiom as a weak form of global choice under the GCH. 19: (with Rodrigo Freire) An axiomatic approach to forcing in a general setting. 18: Ramsey-like Operators. 17: (with Marlene Koelbing, Philipp Schlicht and Wolfgang Wohofsky) Ideal Topologies in Higher Descriptive Set Theory. 16: (with Philipp Lücke) Small Models, Large Cardinals, and Induced Ideals. 15: (with Philipp Lücke and Ana Njegomir) Characterizing Large Cardinals through Neeman's pure side condition forcing. 14: (with Victoria Gitman, Joel Hamkins, Philipp Schlicht and Kameryn Williams) The exact Strength of the Class Forcing Theorem. 13: (with Philipp Lücke and Ana Njegomir) Small Embedding Characterizations for Large Cardinals. 12: (with Regula Krapf and Philipp Schlicht) Sufficient conditions for the forcing theorem, and turning proper classes into sets. 11: (with Philipp Schlicht) A Hierarchy of Ramsey-like cardinals. 10: (with Regula Krapf and Philipp Schlicht) Characterizations of Pretameness and the Ord-cc. 9: (with Philipp Lücke) Simplest possible locally definable Wellorders. 8: (with Regula Krapf, Philipp Lücke, Ana Njegomir and Philipp Schlicht) Class Forcing, the Forcing Theorem and Boolean Completions. 7: Sigma_1-Wellorders without Collapsing. 6: (with David Asperó and Philipp Lücke) Forcing lightface Definable Wellorders without the GCH. 5: (with Philip Welch and Liuzhen Wu) Local Club Condensation and L-likeness. 4: (with Sy-David Friedman and Philipp Lücke) Large Cardinals and Lightface Definable Wellorders without GCH. 3: (with Philipp Lücke) Locally Sigma_1-definable Wellorders of H(kappa^+). 2: (with Sy-David Friedman) A Quasi Lower Bound on the Consistency Strength of PFA. 1: (with Sy-David Friedman) Condensation and Large Cardinals. Dissertation: Condensation and Large Cardinals. Masters Thesis: Absoluteness Results in
Set Theory. Interesting thin sets and Nash-Williams cardinals. (with Philipp Lücke) A countable support iteration for the tree property at aleph_2 and related properties. A short forcing argument for the proper forcing axiom using Magidor's characterization of supercompactness. (with Regula Krapf and Philipp Schlicht) Separation in Class Forcing Extensions. A generalization of the notion of bounded degree for infinite graphs. PFA and Class Forcing. Canonical Function Coding over a Stationary Set. Condensation and Large Cardinals - A Simplified Version of my Dissertation. Compactness of strong logics Infinite Cut and Choose games Ulam style Cut and Choose games A surprising equality between two infinities (p=t) Surreal Numbers Forcing: How to prove Unprovability The Outer Model Programme Large Cardinal Compactness A short talk on Outward Compactness A weak form of global choice under the GCH Asymmetric Cut and Choose games Ramsey-like Operators Uniform Large Cardinal Characterisations and Ideals up to measurability Small Models, Large Cardinals, and Large Cardinal Ideals Characterizing Large Cardinals through Forcing A Hierarchy of Ramsey-like cardinals Small embedding characterizations for large cardinals, and internal large cardinals Ideal Topologies Generalised Topologies on 2^kappa, Silver forcing and Diamond Ideal Topologies The Edinburgh Topology Mathematische Unentscheidbarkeit (Undecidability in Mathematics) The exact Strength of the Class Forcing Theorem How to and how not to turn proper classes into sets Class Forcing and Pretameness Failures of the Forcing Theorem Non-pretame Class Forcing and the Forcing Theorem, the axioms of ZFC and non-definable Class Forcing The Dark Side of Class Forcing Forcing lightface definable Wellorders without the GCH Delta^1_1 subsets of the generalized Baire Space Simplest Possible Wellorders of H(kappa^+) Locally Sigma_1-definable wellorders of H(kappa^+) Large Cardinals and lightface definable Wellorders without the GCH Condensation does not imply Square The Outer Model Programme L-like Models with Large Cardinals and a quasi lower Bound on the Consistency Strength of PFA. Teaching
Publications
In preparation.
Submitted, 2024. pdf
Submitted, 2024. pdf talk slides
Bulletin of Symbolic Logic, 2023. pdf talk slides (general maths audience) talk slides (set theory audience) talk slides (general maths audience)
Journal of Symbolic Logic 88, no. 2, pp. 835-873, 2023. pdf
Archive for Mathematical Logic, 2022. pdf
Bulletin of Symbolic Logic 28, no. 3, pp. 427-450, 2022. pdf
Fundamenta Mathematicae 259, pp. 111-149, 2022. pdf talk slides
Annals of Pure and Applied Logic 173, no. 4, 36 pages, 2022. pdf talk slides 1 talk slides 2 talk slides 3 talk slides 4
Annals of Pure and Applied Logic 172, no. 2, 50 pages, 2021. pdf talk slides 1 talk slides 2
Fundamenta Mathematicae 252, pp. 53-102, 2021. pdf talk slides
Journal of Symbolic Logic 85, no. 3, pp. 869-905, 2020. pdf talk slides
Annals of Pure and Applied Logic 170, no. 2, pp. 251-271, 2019. pdf talk slides
Fundamenta Mathematicae 246, pp. 27-44, 2019. pdf
Fundamenta Mathematicae 242, pp 49-74, 2018. pdf
Annals of Pure and Applied Logic 169, no. 8, pp. 775-802, 2018. pdf
Fundamenta Mathematicae 236, pp. 101-139, 2017. pdf talk slides
Journal of Symbolic Logic 81, no. 4, pp. 1500-1530, 2016. pdf talk slides
Archive for Mathematical Logic 54, issue 3, pp 453-462, 2015. pdf talk slides
Annals of Pure and Applied Logic 166, no. 5, pp. 553-582, 2015. pdf, David Asperó's talk slides
Journal of Symbolic Logic 80, no. 4, pp. 1361-1378, 2015. pdf, talk slides
Journal of Symbolic Logic 80, issue 1, pp 251-284, 2015. pdf, talk slides
Fundamenta Mathematicae 226, pp 221-236, 2014. pdf, talk slides
Transactions of the AMS 366, pp 4021-4065, 2014. pdf, talk slides
Fundamenta Mathematicae 215, no. 2, pp 133-166, 2011. pdf, info
(2010, advisor: Sy D. Friedman) pdf, info
(2007, advisor: Sy D. Friedman) pdf
Unpublished Notes
(2024) pdf
(2020) pdf
(2019) pdf
(2017) pdf
(2014) pdf
(2013) pdf
(2013) pdf, info
(2013) pdf, info
Talks
General Math Audience Talks
TU Wien Algebra seminar, Vienna, 15.03.2024
TU Wien Algebra seminar, Vienna, 04.11.2022 --> pdf
VCU Analysis, Logic and Physics Seminar, 08.10.2021 --> pdf
Habilitation Colloquium, Bonn, 31.01.2019
Basic Notions Seminar, Bonn, 25.10.2016 (following slides by Yurii Khomskii)
Basic Notions Seminar, Bonn, 18.11.2015 (Part II of a two-part talk, part I by Regula Krapf).
Norwich Pure Maths Seminar, 28.04.2014 --> pdf
Compactness Principles
Seventh Workshop on generalised Baire spaces, Bristol, 10.02.2024 --> pdf
KGRC set theory seminar, Vienna, 22.11.2022
Weak forms of Global Choice
KGRC set theory seminar, Vienna, 10.01.2023 and 17.01.2023 (two part talk)
Infinite Games
Barcelona set theory seminar, 25.05.2022; New York set theory seminar, 11.11.2022 --> pdf
Large Cardinals
Torino/Udine logic seminar, 20.11.2020; Set Theory in the UK workshop, 04.12.2020; Kurt Gödel Research Center, 17.12.2020 --> pdf
New York Set Theory Seminar, 10.07.2020 --> pdf
Bonn Logic Seminar, 23.10.2018; European Set Theory Conference, Vienna, 05.07.2019 --> pdf
Set Theory Today Conference, Vienna, 10.09.2018 --> pdf
Bristol Set Theory Seminar, 07.03.2017
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
Bristol Logic and Set Theory Seminar, 10.06.2020 --> pdf
Udine Logic Seminar, 29.05.2020 --> pdf
Udine Logic Seminar, 01.04.2020 --> pdf
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
Antrittsvorlesung, Dies Academicus, University of Bonn, 04.12.2019 --> pdf (in German)
Class Forcing
Bonn Logic Seminar, 23.10.2017 --> pdf
Bonn Logic Seminar, 24.10.2016
Hamburg Logic Seminar, 30.05.2016
European Set Theory Conference, Cambridge, 25.08.2015 --> pdf
Kurt Gödel Research Center, Vienna, 27.05.2015
Bristol Logic Seminar, 10.03.2015
Locally Definable Wellorders
Bonn Logic Seminar, 09.11.2015
Amsterdam workshop on Set Theory, 03.11.2014 --> pdf
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
ESI Workshop on Forcing and Large Cardinals, Vienna, 23.09.2013
Kurt Gödel Research Center, Vienna, 10.01.2013; Bristol Logic Seminar, 11.03.2013 --> pdf
Condensation and the Outer Model Programme
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
Oxford Logic Seminar, 07.02.2013 --> pdf
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
Current Teaching
at the Technical University of Vienna:
autumn 2024:
Algebra 2 - Lecture and Exercises
Past Teaching
at the Technical University of Vienna:
spring 2024: Algebra (with Michael Pinsker)
autumn 2023: Algebra 2 - Lecture (with Michael Pinsker) and Exercises
spring 2023: Linear Algebra 2
at the University of Udine:
autumn 2021: PhD course Infinite games and (generic) large cardinals
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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Update log here.