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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:20 years of K-triviality - Andre Nies (University
of Auckland)
DTSTART;TZID=Europe/London:20220607T133000
DTEND;TZID=Europe/London:20220607T143000
UID:TALK174800AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/174800
DESCRIPTION:In June 2012\, I gave a talk at Chicheley Hall ent
itled &ldquo\;10 Years of Triviality&rdquo\;\, in
connection with the Turing year. The current talk
will trace the developments in the area of K-trivi
al sets of natural numbers that took place since t
hen. Several further characterisation of this clas
s were obtained\, taking the total to 18 or so. Th
e covering problem (whether above each K-trivial t
here is an incomplete ML-random) was solved in the
affirmative by a collaboration of seven researche
rs in the same year 2012. Later on\, researchers a
ddressed the internal structure of the class of K-
trivial sets\, using a reducibility coarser than T
uring&rsquo\;s: A is ML-below B if every ML-random
computing B also computes A. It turns out that th
e K-trivial sets are well behaved under ML-reducib
ility\; in particular\, there is a complete K-triv
ial\, and there are no minimal pairs. Sadly\, we d
on&rsquo\;t know to this day whether ML-reducibili
ty is arithmetical.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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