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SUMMARY:Classification problem for effective structures - Ekaterina Fokina
  (Vienna University of Technology)
DTSTART:20220609T123000Z
DTEND:20220609T133000Z
UID:TALK174830@talks.cam.ac.uk
DESCRIPTION:In this talk we will review several approaches to study the co
 mplexity of classifying effective structures up to isomorphism or another 
 equivalence relation. Calculating the complexity of the set $E_\\equiv(K)$
  of pairs of indices corresponding to $\\equiv$-equivalent computable stru
 ctures from a fixed class $K$ is one of the approaches. One can use 1-dime
 nsional or 2-dimensional versions of $m$-reducibility to establish the com
 plexity of such index sets. According to this approach\, a class is nicely
  classifiable if the set $E_\\equiv(K)$ has hyperarithmetical complexity (
 provided the class $K$ itself is hyperarithmetical). Another approach is t
 o classify structures on-the-fly. We call a class classifiable in this sen
 se if we can uniquely (up to a fixed equivalence relation) identify each s
 tructure from the class after observing a finite piece of the structure.
LOCATION:Seminar Room 1\, Newton Institute
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