Game comonads, FVM theorems, and bilinear maps

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• Dan Marsden, University of Oxford
• Friday 06 May 2022, 14:00-15:00
• SS03.

If you have a question about this talk, please contact Jamie Vicary.

Model comparison games such as the Ehrenfeucht-Fraisse game or the pebble game are fundamental tools in finite model theory, used to establish equivalence between models for a specified logic. The recently introduced game comonads give a novel categorical semantics for these these model comparison games.

A Feferman-Vaught-Mostowski (FVM) theorem describes how logical equivalence behaves under composition and transformation of models. In this talk, we will discuss FVM theorems from the point of view of game comonads. In particular, we will highlight some perhaps surprising connections to classical results in monad theory, abstracting the notion of bilinear maps.

We shall give a brief high-level introduction to the game comonads, and no prior knowledge of these recent constructions will be assumed.

(The talk covers joint work with Tomas Jakl and Nihil Shah.)

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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