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SUMMARY:Degree spectra of computable functions on natural numbers with sta
 ndard order - Dariusz Kalociński (Polish Academy of Sciences)
DTSTART:20220610T101500Z
DTEND:20220610T111500Z
UID:TALK174845@talks.cam.ac.uk
DESCRIPTION:The degree spectrum of a computable relation on a computable s
 tructure consists of all Turing degrees of the images of the relation acro
 ss all computable copies of the structure. Investigation of the degree spe
 ctra of computable relations on the computable structure consisting of nat
 ural numbers and the standard order has exhibited spectra such as the triv
 ial one\, all c.e. degrees and all  degrees. I will review recent results 
 regarding the restriction of this problem to graphs of unary total recursi
 ve functions. This approach has led\, among others\, to the the negative a
 nswer to one of the questions posed by M. Wright\, namely whether the afor
 ementioned spectra exhaust all possibilities. The talk will be based on a 
 joint work with N. Bazhenov and M. Wrocławski.
LOCATION:Seminar Room 1\, Newton Institute
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