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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        <p>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.</p>\n        <p>\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.</p>\n    \n       
  <p>For abstracts and more information, see <a tar
 get="_blank" href="http://www.staff.science.uu.nl/
 ~ooste110/seminar.html">http://www.staff.science.u
 u.nl/~ooste110/seminar.html</a> or contact Benno v
 an den Berg (<a class="email">bennovdberg <span cl
 ass="at">at</span> gmail.com</a>).</p>\n    
URL:/NewsandEvents/Archives/2016/newsitem/7452/22-
 June-2016-Colloquium-on-Mathematical-Logic-Fabio-P
 asquali
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