Universiteit van Amsterdam

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Institute for Logic, Language and Computation

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22 June 2016, Colloquium on Mathematical Logic, Fabio Pasquali

Speaker: Fabio Pasquali
Title: Choice in triposes
Date: Wednesday 22 June 2016
Time: 16:00-17:00
Location: Room 610 of the Mathematics (Hans Freudenthal) building, Budapestlaan 6, Utrecht

Maietti and Rosolini generalized the notion of exact completion of a category with finite limits to that of elementary quotient completion of hyperdoctrines. A hyperdoctrine will be denoted by (C,P) and can be thought of as a many-sorted logic P where sorts are objects of the category C. The elementary quotient completion of (C,P), denoted by (Cq,Pq), is a new hyperdoctrine whose base Cq is closed under effective quotients of equivalence relations expressed in the logic of Pq.

In this talk we focus on triposes, a special class of hyperdoctrines, introduced in by Hyland, Johnstone and Pitts with the purpose (among others) of freely creating an elementary topos out of any given tripos. This mentioned construction is known under the name of tripos-to-topos construction. We characterize when the tripos-to-topos construction factors through an elementary quotient completion. We will show that this happens if and only if the starting tripos validates a form of choice, which we call rule of epsilon choice as it is inspired by Hilbert's epsilon operator.

For abstracts and more information, see http://www.staff.science.uu.nl/~ooste110/seminar.html or contact Benno van den Berg ().

Please note that this newsitem has been archived, and may contain outdated information or links.