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SUMMARY:Steffen Lempp (U of Wisconsin)
DTSTART:20201022T180000Z
DTEND:20201022T190000Z
DTSTAMP:20260423T035747Z
UID:OLS/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/31/">The
  Turing Degrees: On the Order Dimension of and Embeddings into the Turing 
 Degrees</a>\nby Steffen Lempp (U of Wisconsin) as part of Online logic sem
 inar\n\n\nAbstract\nIn joint work with Higuchi\, Raghavan and Stephan\, we
  show that the order dimension of any locally countable partial ordering (
 P\, <) of size κ+\, for any κ of uncountable cofinality\, is at most κ.
 \nIn particular\, this implies that it is consistent with ZFC that the dim
 ension of the Turing degrees under partial ordering can be strictly less t
 han the continuum. (Kumar and Raghavan have since shown that it can also b
 e continuum\, thus the order dimension of the Turing degrees is independen
 t of ZFC.)\nThis is closely related to an old question of Sacks from 1963 
 about whether the Turing degrees form a universal locally countable partia
 l order of size continuum.\n
LOCATION:https://researchseminars.org/talk/OLS/31/
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