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SUMMARY:Vittorio Bard (Università degli Studi di Torino)
DTSTART:20200602T140000Z
DTEND:20200602T150000Z
DTSTAMP:20260404T131151Z
UID:CTA/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CTA/7
 /">A local approach towards uniform Martin’s conjecture</a>\nby Vittorio
  Bard (Università degli Studi di Torino) as part of Computability theory 
 and applications\n\n\nAbstract\nIn 1967 Sacks asked whether there is degre
 e invariant r.e. operator that maps x to a solution to Post's problem rela
 tivized for x. In 1975\, Lachlan proved that the answer is no if we requir
 e the operator to be degree invariant in a uniform way.\nSack's question c
 an be considered the forefather of Martin's conjecture\, a foundamental op
 en problem that hypothizes that degree invariant functions under AD have l
 imited possibilities of behavior. Following Lachlan's example\, in the lat
 e 80s Slaman and Steel proved Martin's conjecture for unifromly degree inv
 ariant functions.\nWe will show that half of this result is actually the c
 onsequence of phenomena that unifromly degree invariant functions already 
 manisfest on single Turing degrees. We also present a joint result with Pa
 trick Lutz\, in which we show that Lachlan's result arises locally\, too.\
 n
LOCATION:https://stable.researchseminars.org/talk/CTA/7/
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