BEGIN:VCALENDAR VERSION:2.0 PRODID:ILLC Website X-WR-TIMEZONE:Europe/Amsterdam BEGIN:VTIMEZONE TZID:Europe/Amsterdam X-LIC-LOCATION:Europe/Amsterdam BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19700329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19701025T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:/NewsandEvents/Archives/2016/newsitem/7452/22- June-2016-Colloquium-on-Mathematical-Logic-Fabio-P asquali DTSTAMP:20160609T000000 SUMMARY:Colloquium on Mathematical Logic, Fabio Pa squali ATTENDEE;ROLE=Speaker:Fabio Pasquali DTSTART;TZID=Europe/Amsterdam:20160622T160000 DTEND;TZID=Europe/Amsterdam:20160622T170000 LOCATION:Room 610 of the Mathematics (Hans Freuden thal) building, Budapestlaan 6, Utrecht DESCRIPTION:Maietti and Rosolini generalized the n otion of exact completion of a category with finit e limits to that of elementary quotient completion of hyperdoctrines. A hyperdoctrine will be denote d 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), deno ted by (Cq,Pq), is a new hyperdoctrine whose base Cq is closed under effective quotients of equivale nce relations expressed in the logic of Pq. In t his talk we focus on triposes, a special class of hyperdoctrines, introduced in by Hyland, Johnstone and Pitts with the purpose (among others) of free ly creating an elementary topos out of any given t ripos. This mentioned construction is known under the name of tripos-to-topos construction. We chara cterize when the tripos-to-topos construction fact ors through an elementary quotient completion. We will show that this happens if and only if the sta rting tripos validates a form of choice, which we call rule of epsilon choice as it is inspired by H ilbert's epsilon operator. For abstracts and more information, see http://www.staff.science.uu.nl/~ ooste110/seminar.html or contact Benno van den Ber g (bennovdberg at gmail.com). X-ALT-DESC;FMTTYPE=text/html:\n
Maietti and Rosolini generalized the notion of exact compl etion of a category with finite limits to that of elementary quotient completion of hyperdoctrines. A hyperdoctrine will be denoted by (C,P) and can b e thought of as a many-sorted logic P where sorts are objects of the category C. The elementary quot ient completion of (C,P), denoted by (Cq,Pq), is a new hyperdoctrine whose base Cq is closed under e ffective quotients of equivalence relations expres sed in the logic of Pq.
\n\n In this talk we focus on triposes, a special class of hyperdoctrines, introduced in by Hyland, Johns tone and Pitts with the purpose (among others) of freely creating an elementary topos out of any giv en tripos. This mentioned construction is known u nder 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 th e starting tripos validates a form of choice, whic h we call rule of epsilon choice as it is inspired by Hilbert's epsilon operator.
\n \nFor abstracts and more information, see http://www.staff.science.u u.nl/~ooste110/seminar.html or contact Benno v an den Berg (bennovdberg at gmail.com).
URL:/NewsandEvents/Archives/2016/newsitem/7452/22- June-2016-Colloquium-on-Mathematical-Logic-Fabio-P asquali END:VEVENT END:VCALENDAR