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From the Around Toposes Blog: A talk on proof-theoretic aspects of Grothendieck topologies


Olivia Caramello
(@ocaramello)
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Tomorrow (Monday 22 November 2021, at 9:40 Central European Time) I will give a talk on "Deductive systems and Grothendieck topologies" for the Dagstuhl Seminar Geometric Logic, Constructivisation, and Automated Theorem Proving.

The abstract is as follows:

I will show that the classical proof system of geometric logic over a given geometric theory is equivalent to new proof systems based on the notion of Grothendieck topology. These equivalences result from a proof-theoretic interpretation of the duality between the quotients of a given geometric theory and the subtoposes of its classifying topos. Interestingly, these alternative proof systems turn out to be computationally better-behaved than the classical one for many purposes, as I will illustrate by discussing a few selected applications.

To attend the talk, you may click here.


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