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SUMMARY:Dino Rossegger (UC Berkeley)
DTSTART:20211102T200000Z
DTEND:20211102T210000Z
DTSTAMP:20260423T004821Z
UID:CTA/70
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/70/">New
  examples of degrees of categoricity</a>\nby Dino Rossegger (UC Berkeley) 
 as part of Computability theory and applications\n\n\nAbstract\nWe confirm
  a conjecture by Csima and Ng that if $\\mathbf d$ is a Turing degree with
  $\\mathbf 0^{(\\alpha)}\\leq \\mathbf d\\leq \\mathbf 0^{(\\alpha+1)}$ fo
 r some computable $\\alpha$\, then $\\mathbf d$ is a degree of categoricit
 y. For $\\alpha\\geq 2$ we modify a technique developed by Dan Turetsky to
  code paths through trees into the automorphisms of structures. This allow
 s us to obtain structures with these degrees of categoricity that are rigi
 d and have computable dimension $2$. For both properties\, this is the lea
 st $\\alpha$ where we can obtain this result. Goncharov showed that if a s
 tructure is $\\mathbf 0'$-computably categorical\, then it can not have fi
 nite computable dimension other than $1$. Bazhenov and Yamaleev constructe
 d a properly d-c.e.\\ degree $\\mathbf d$\, that is not the degree of cate
 goricity of a rigid structure. We combine their construction with true sta
 ges to obtain a degree $\\mathbf d$\, $\\mathbf 0'<\\mathbf d< \\mathbf 0'
 '$ that is not the degree of categoricity of a rigid structure. This is jo
 int work with Barbara Csima.\n
LOCATION:https://researchseminars.org/talk/CTA/70/
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