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SUMMARY:Steffen Lempp (University of Wisconsin-Madison)
DTSTART:20210331T010000Z
DTEND:20210331T020000Z
DTSTAMP:20260423T005727Z
UID:CTA/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/52/">Dec
 idability and Undecidability in the Enumeration Degrees</a>\nby Steffen Le
 mpp (University of Wisconsin-Madison) as part of Computability theory and 
 applications\n\n\nAbstract\nFor most “natural” degree structures\, the
  full first-order theory (in the language of partial ordering) is as compl
 icated full first or second-order arithmetic\, so it is natural to try to 
 determine the quantifier level at which undecidability starts. For most 
 “natural” degree structures\, this seems to happen when we move from t
 he AE-theory to the EAE-theory.\nI will survey some of the results from th
 e past fifty years in this area and then focus on a new joint result with 
 Slaman and M. Soskova on the degree structure of the enumeration degrees: 
 By proving a strong embedding result for finite distributive lattices into
  intervals of the enumeration degrees\, we obtain the undecidability of th
 e EAE-theory\, and a partial decidability result for the AE-theory\, namel
 y\, for the extension of embeddings problem.\n
LOCATION:https://researchseminars.org/talk/CTA/52/
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