Research

I finished my PhD in set theory at University of Bonn (January 2017) under the supervision of Prof. Dr. Peter Koepke. In my PhD project I studied the foundations of class forcing, in particular the forcing theorem and pretameness. In a joint project with Peter Holy and Philipp Schlicht I have charactarized pretameness in terms of many fundamental properties of forcing notions such as the existence of Boolean completions, the forcing theorem and the existence of nice names for sets of ordinals.

I am also interested in general logic (in particular Gödel's Incompleteness Theorems), history of mathematics (in particular set theory) and mathematics education (in particular in the introductory phase of the university level). I am currently an associated member of the forcing project lead by Carolin Antos at university of Konstanz, working on the history of the forcing method after its discovery by Paul J. Cohen in the 1960ies.

Publications

Papers and Preprints

  • (mit Michael Liebendörfer) Was bewirkt die Pflichtabgabe von Übungsaufgaben in der Hochschulmathematik? Ein empirischer Vergleich. In preparation.

  • (mit Lorenz Halbeisen, Marc Lischka, Salome Schumacher und Giovanni Sommaruga) Zahringer Logics - new approaches to multi-valued modal logics. Submitted.
  • "Wie kommt man drauf? - Ergebnisse aus einem Tutorium über die Methoden des mathematischen Arbeitens. To be published in Beiträge zum Mathematikunterricht 2019.
  • Auswirkungen einer aktiven Beteiligung am Übungsbetrieb auf den Studienerfolg und mögliche Unterstützungsmaßnahmen in der Studieneingangsphase. To be published in Beiträge zum Mathematikunterricht 2018.

  • (with Ioanna Dimitriou, Peter Koepke and Michael Möllerfeld) Set theory has the same strength as second-order arithmetic with regularity properties . Submitted.
  • (with Peter Holy and Philipp Schlicht) Sufficient conditions for the forcing theorem, and turning proper classes into sets. Accepted for the Fundamenta Mathematicae.
  • (with Peter Holy and Philipp Schlicht) Characterizations of Pretameness and the Ord-cc.  Annals of Pure and Applied Logic, no. 8. pp. 775–802, 2018.

Books

  • (with Lorenz Halbeisen) Gödel's Theorems and Zermelo's Axioms. In preparation (Birkhäuser Verlag).
  • Elmentare Grundlagen der Hochschulmathematik - Fachlich und methodisch mit Online-Selbsttests. In preparation (Springer Verlag).
  • Unendlichkeit in den Grundlagen der Mathematik (working title). In preparation (Springer Verlag).

Theses

  • Class Forcing and Second-Order Arithmetic. PhD thesis, University of Bonn, 2016 (Defense in 2017).
  • A Complete Proof of Incompleteness. Master thesis, University of Zürich, 2013.

    Unpublished Notes

    • (with Peter Holy and Philipp Schlicht) Separation in Class Forcing Extensions.

    Talks

    Upcoming Talks

    • "Wie kommt man drauf? - Ergebnisse aus einem Tutorium über die Methoden des mathematischen Arbeitens. GDM-Tagung, University of Regensburg, March 2019.

    Past Talks

    • Class Forcing and Second-Order Arithmetic. Colloquium Logicum 2018, University of Bayreuth, September 2018.
    • An Introduction to Forcing. UnDecidability: DMV-Studierendenkolleg, June 2018.
    • An Introduction to Forcing. FMV: Foundations of Mathematics - Modern Views, Munich, April 2018.
    • Auswirkungen einer aktiven Beteiligung am Übungsbetrieb auf den Studienerfolg und mögliche Unterstützungsmaßnahmen in der Studieneingangsphase. GDMV-Tagung, University of Paderborn, March 2018.
    • Characterizations of Pretameness. Workshop Forcing and Philosophy, University of Konstanz, January 2018.
    • Ich bin kein Titel. Paradoxien in der Logik und ihre Bedeutung für die Hochschuldidaktik. Oberseminar Mathematikdidaktik, University of Mainz, June 2017.
    • (Non-)Existence of Boolean Completions in Class Forcing. Oberseminar Mathematische Logik, University of Hamburg, January 2017.
    • Class Forcing over Models of Second-order Arithmetic and Preservation of the Perfect Set Property. Oberseminar Mathematische Logik, University of Bonn, December 2016.
    • An Introduction to Forcing. FOMUS - Foundations of Mathematics, Univalent Foundations and Set Theory (Conference). Bielefeld, July 2016.
    • Characterizations of Pretameness and the Ord-cc. Oberseminar Mathematische Logik, University of Bonn, December 2015.
    • Pi_1°1-Determinacy and Sharps in Second-Order Arithmetic. Oberseminar Mathematische Logik, University of Bonn, May 2015.
    • Ich bin kein Titel. Unvollständigkeit, Unentscheidbarkeit, Undefinierbarkeit. Unfehlbarkeit durch Formalismus? (Conference) Bonn, March 2015.
    • The Pseudointersection Number and the Tower Number. Oberseminar Mathematische Logik, University of Freiburg, April 2013.

    I also enjoy giving talks about various topics in logic and set theory for a general (mathematical) audience. In particular I have given many talks in the Basic Notions Seminar at University of Bonn and at the Oberseminar Mathematik and the Kolloquium at University of Koblenz-Landau, Campus Koblenz. Some examples are:

    • Determinacy of Infinite Games
    • Gödel's Theorems: Incompleteness, Undecidability and Undefinability.
    • The Independence of the Continuum Hypothesis
    • The Axiom of Choice