BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Vittorio Bard (Università degli Studi di Torino)
DTSTART:20200602T140000Z
DTEND:20200602T150000Z
DTSTAMP:20260423T004916Z
UID:CTA/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/7/">A lo
 cal approach towards uniform Martin’s conjecture</a>\nby Vittorio Bard (
 Università degli Studi di Torino) as part of Computability theory and app
 lications\n\n\nAbstract\nIn 1967 Sacks asked whether there is degree invar
 iant r.e. operator that maps x to a solution to Post's problem relativized
  for x. In 1975\, Lachlan proved that the answer is no if we require the o
 perator to be degree invariant in a uniform way.\nSack's question can be c
 onsidered the forefather of Martin's conjecture\, a foundamental open prob
 lem that hypothizes that degree invariant functions under AD have limited 
 possibilities of behavior. Following Lachlan's example\, in the late 80s S
 laman and Steel proved Martin's conjecture for unifromly degree invariant 
 functions.\nWe will show that half of this result is actually the conseque
 nce of phenomena that unifromly degree invariant functions already manisfe
 st on single Turing degrees. We also present a joint result with Patrick L
 utz\, in which we show that Lachlan's result arises locally\, too.\n
LOCATION:https://researchseminars.org/talk/CTA/7/
END:VEVENT
END:VCALENDAR