My name is Dominik and I'm a PhD student at the Saarbrücken Graduate School of Computer Science and the Programming Systems Lab.

I did my Bachelor's Thesis and a Research Immersion Lab on set theory formalised in Coq. I obtained my Master's degree from the University of Oxford with a thesis on intersection type systems and nominal automata. I recently finished a second Bachelor's degree in cultural studies with a thesis on foundations of mathematics hosted by the philosophy department.

I'm broadly interested in constructive and computational logic and its connections to the foundations and philosophy of mathematics. Currently, I'm mostly working on mechanised first-order logic and categorical axiomatisations of second-order ZF, both using the Coq proof assistant.

**Trakhtenbrot's Theorem in Coq: Finite Model Theory through the Constructive Lens** *(pdf)*

* Dominik Kirst, Dominique Larchey-Wendling*

Submitted for review.

**Synthetic Undecidability and Incompleteness of First-Order Axiom Systems in Coq** *(pdf)(slides)(video)*

* Dominik Kirst, Marc Hermes*

ITP 2021, Rome, Italy, 2021.

**The Generalised Continuum Hypothesis Implies the Axiom of Choice in Coq** *(pdf)(slides)(video)*

* Dominik Kirst, Felix Rech*

CPP 2021, Copenhagen, Denmark, 2021.

**Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory (Extended Version)** *(pdf)*

* Yannick Forster, Dominik Kirst, Dominik Wehr*

Journal of Logic and Computation, 2021

**Trakhtenbrot's Theorem in Coq: A Constructive Approach to Finite Model Theory** *(pdf)(slides)(video)*

* Dominik Kirst, Dominique Larchey-Wendling*

IJCAR 2020, Paris, France, 2020.

**Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory** *(pdf)(slides)*

* Yannick Forster, Dominik Kirst, Dominik Wehr*

LFCS 2020, Deerfield Beach, Florida, USA, 2020.

**On Synthetic Undecidability in Coq, with an Application to the Entscheidungsproblem** *(pdf)(slides)*

*Yannick Forster, Dominik Kirst, Gert Smolka*

CPP 2019, Cascais, Portugal, 2019.

**Categoricity Results and Large Model Constructions for Second-Order ZF in Dependent Type Theory** *(pdf)*

*Dominik Kirst and Gert Smolka*

Journal of Automated Reasoning, 2018.

**Large Model Constructions for Second-Order ZF in Dependent Type Theory** *(pdf)**(slides)*

*Dominik Kirst and Gert Smolka*

CPP 2018, Los Angeles, California, USA, 2018.

**Categoricity Results for Second-Order ZF in Dependent Type Theory** *(pdf)**(slides)*

*Dominik Kirst and Gert Smolka*

ITP 2017, Brasilia, Brazil, 2017.

**The Generalised Continuum Hypothesis Implies the Axiom of Choice in HoTT** *(pdf)(slides)(video)*

*Dominik Kirst, Felix Rech*

Submitted for review.

**A Toolbox for Mechanised First-Order Logic** *(pdf)(slides)(video)*

*Johannes Hostert, Mark Koch, Dominik Kirst*

Submitted for review.

**Synthetic Undecidability Proofs in Coq:
Entscheidungsproblem, Trakhtenbrotâ€™s Theorem, First-Order Axiom Systems**

Talk at the Computer Science Theory Seminar, Tallinn, Estonia, 2020.

**Towards Extraction of Continuity Moduli in Coq** *(pdf)(slides)*

*Yannick Forster, Dominik Kirst, Florian Steinberg*

Types 2020, Turin, Italy, 2020.

**A Coq Library of Undecidable Problems** *(pdf)*

*Yannick Forster, Dominique Larchey-Wendling, Andrej Dudenhefner, Edith Heiter, Dominik Kirst, Fabian Kunze, Gert Smolka, Simon Spies, Dominik Wehr, Maximilian Wuttke*

CoqPL 2020, New Orleans, USA, 2020.

**Foundations of Mathematics: A Discussion of Sets and Types** *(pdf)*

*Dominik Kirst*

Bachelor's Thesis, Department of Philosophy, Saarland University, 2018.

**Intersection Type Systems Corresponding to Nominal Automata** *(pdf)*

*Dominik Kirst*

Master's Thesis, Lady Margaret Hall, University of Oxford, 2016.

**Formalised Set Theory: Well-Orderings and the Axiom of Choice** *(pdf)*

*Dominik Kirst*

Bachelor's Thesis, Programming Systems Lab, Saarland University, 2014.

Mark Koch, 2021, Bachelor's thesis (ongoing):

Mechanization of Second-order Logic

Johannes Hostert, 2021, Bachelor's thesis (ongoing), co-advised with Andrej Dudenhefner:

The Undecidability of First-order Logic over Small Signatures

Christian Hagemeier, 2020, Bachelor's thesis, co-advised with Holger Sturm:

Formalizing Intuitonistic Epistemic Logic in Coq

Marc Hermes, 2020, Master's thesis (ongoing), co-advised with Moritz Weber:

Formalisation of Peano Arithmetic in Coq

Felix Rech, 2019, Master's thesis:

On the Generalized Continuum Hypothesis in Coq

Dominik Wehr, 2019, Bachelor's thesis, co-advised with Yannick Forster:

Formalising Completeness of First-Order Logic

Leonhard Staut, 2017, Bachelor's thesis:

Nu-Trees in Coq

Winter 2020/2021 | AdvisorAdvanced Coq Programming Advanced Course, Programming Systems Lab. |

Summer 2020 | Teaching AssistantIntroduction to Computational Logic Core Course, Programming Systems Lab. |

Summer 2020 | AdvisorFunktionale Programmierung Proseminar, Programming Systems Lab. |

Summer 2019 | Teaching AssistantIntroduction to Computational Logic Core Course, Programming Systems Lab. |

Winter 2018/2019 | Organiser, Advisor, and LecturerFoundations of Mathematics Seminar, Programming Systems Lab. |

Winter 2018/2019 | CoachMathematics Precourse Saarland University. |

Summer 2018 | Teaching AssistantIntroduction to Computational Logic Core Course, Programming Systems Lab. |

Summer 2018 | AdvisorAdvanced Coq Programming Advanced Course, Programming Systems Lab. |

Winter 2017/2018 | Advisor Category Theory Seminar, Programming Systems Lab. |

Summer 2017 | Advisor and LecturerCategory Theory Seminar, Programming Systems Lab. |

Summer 2014 | Student TAIntroduction to Computational Logic Core Course, Programming Systems Lab. |

Winter 2013/2014 | Student TATheoretical Computer ScienceBasic Course, Programming Systems Lab. |

Summer 2013 | Student TAProgramming 2Basic Course, Compiler Design Lab. |

Winter 2012/2013 | Student TAProgramming 1 Basic Course, Programming Systems Lab. |

Summer 2012 | Student TAMathematics Precourse Saarland University. |

Mail: | dominik.kirst at cs.uni-saarland.de |

Adress: | Saarland University, Saarland Informatics Campus E1 3, Rm 523 66123 Saarbrücken |

Phone: | +49 (0)681 / 302-5626 |