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  • Tomáš Jakl (Institute of Mathematics of the Czech Academy of Sciences and Czech Technical University):

    A Personal Perspective on the Game Comonad Programme

    24.04.2024 16:00Room 318 (live) and ZOOM @ Institute of Computer Science
    Pod Vodárenskou věží 2
    Praha, 182 00
    Applied Mathematical Logic Seminar

    Finite model theory's main focus is in the study of logics that have close connections to descriptive complexity. One of the main tools to show e.g. inexpressibility of certain logics are model comparison games, such as the Ehrenfeucht--Fraisse, pebble, and bisimulation games. The main idea behind game comonads comes from the observation that plays in a typical model comparison game can be encoded into a semantics construction which, moreover, admit the structure of a comonad on the category of relational structures. This allows one to treat model comparison games abstractly, in the language of category theory. In this talk, I give an overview of the game comonad programme, its recent development and open problems. Concretely, I will list the most notable game comonads and explain their relationship with various logic fragments. I will also overview the recent model-theoretic results proved in this framework. I shall also explain how the various different model comparison games can be viewed as an instance of a game in arboreal categories, which are used to axiomatise common features of Eilenberg--Moore categories of coalgebras of game comonads.

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