Mathematik und Statistik
Schwerpunkt Reelle Geometrie und Algebra > Dr. Merlin Carl


Published articles:

  • (with Philipp Schlicht) Randomness via infinite computation and effective descriptive set theory. To appear in the Journal of Symbolic Logic.
  • (with Philipp Schlicht and Philip Welch) Recognizable sets and Woodin cardinals: Computation beyond the constructible universe. To appear in the Annals of Pure and Applied Logic.
  • (with Bruno Durand, Gregory Lafitte and Sabrina Ouazzani) Admissibles in Gaps. Lecture Notes in Computer Science, Proceedings of the CiE 2017
  • (with Philipp Schlicht) The recognizability strength of infinite time Turing machines with ordinal parameters. Lecture Notes in Computer Science, Proceedings of the CiE 2017
  • (with Benjamin Rin and Benedikt Löwe) Koepke machines and satisfiability for infinitary propositional languages. Lecture Notes in Computer Science, Proceedings of the CiE 2017
  • An Invitation to Infinitary Computability. (Extended Abstract) Proc. Appl. Math. Mech. 16 (2016)
  • (with Paola D'Aquino and Salma Kuhlmann) On the value group of a model of Peano Arithmetic. Forum Mathematicum 29(4), pp. 951-957.
  • Generalized Effective Reducibility. Lecture Notes in Computer Science, Special Issue for CiE 2016
  • Structures Associated with Real Closed Fields and the Axiom of Choice. To appear in the Bulletin of the BMS.
  • Infinite Time Recognizability from Random Oracles and the Recognizable Jump Operator. Computablity. The Journal of the Association CiE. vol. 6, no. 3, pp. 223-247, 2017
  • Randomness and Degree Theory for Infinite Time Register Machines. Computability, vol. 5, no. 2, pp. 181-196, 2016
  • ITRM-recognizability from Random Oracles. Lecture Notes in Computer Science, Special Issue for CiE 2015
  • Optimal Results on Recognizability for Infinite Time Register Machines. J. of Symbolic Logic, Vol. 80, Issue 04, pp 1116-1130 (2015)
  • with Philipp Schlicht: Infinitary Computations with Random Oracles. Notre Dame Journal of Formal Logic, Vol. 58, No 2, pp 249-270 (2017)
  • Algorithmic Randomness for Infinite Time Register Machines. Lecture Notes in Computer Science, Special Issue for CiE 2014
  • The Lost Melody Phenomenon. In: Infinity, Computability, and Metamathematics. Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch. Tributes Vol. 23
  • The distribution of ITRM-recognizable reals. Annals of Pure and Applied Logic, Vol. 165, Issue 9 (2014).
  • with B.Z. Moroz: A polynomial encoding provability in pure mathematics (an explicit construction), Bulletin of BMS
  • with B.Z. Moroz: On a Diophantine representation of the predicate of provability, Zapiski Nauchnykh Seminarov POMI (English version in Journal of the Mathematical Sciences, Vol. 199, No. 1)
  • with Tim Fischbach, Peter Koepke, Miriam Nasfi, Russell Miller and Gregor Weckbecker: „The basic theory of Infinite Time Register Machines“
    Arch. Math. Logic 49:249–273 No. 4, 850-856 (2010)
  • with Peter Koepke: Interpreting Naproche - An algorithmical approach to the derivation-indicator view.
    Im Konferenzband zu: AISB 2010 – Symposium on mathematical practice and cognition (Leicester)
  • A computational approach to an alternative working environment for the constructible universe
    Proceeding CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
  • Towards a Church-Turing-Thesis for Infinitary Computations.
    Electronic Proceedings for CiE 2013

  • Submitted

    See also my KOPS site.
    For further preprints, see also my Arxiv page


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    Reviews for Zentralblatt MATH

    Habilitation Thesis:

    My habilitation thesis is cumulative and consists of the following of the above articles:


    Alternative Finestructural and Computational Approaches to Constructibility
    Dissertation an der Rheinischen Friedrich-Wilhelms-Universität Bonn (2011)
    Advisor: P. Koepke

    Diploma thesis:

    Formale Mathematik und diophantische Gleichungen. Advisors: B.Z. Moroz and P. Koepke.


    TimeBall, a little puzzle video game featuring time travel written in Prolog. If you like it and have a good idea for an extra level, write me an E-mail! To play it, download the following three files and safe them in one folder: File 1 File 2 File 3
    Disclaimer: The author of the program offered for download here is not responsible for any damage of soft-or hardware that may occur through the use of the program.
    You will also need SWI-Prolog with XPCE-extension, which you can download here .
    To start the game, doubleclick TimeBallv4c.pl. Prolog will start automatically. When it is done grumping about the implementation, enter `time_ball.' and press Enter. The game should now start.
    A brief description of the game and how to play can be found here .
    The author of this software does not grant permission to distribute the program for profit in any form. Non-profit distribution of the program is acceptable without prior written notice, providing that the program is not modified in any way, and the author is clearly acknowledged.