BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Java Darleen Villano (University of Connecticut)
DTSTART:20241024T180000Z
DTEND:20241024T190000Z
DTSTAMP:20260423T035615Z
UID:OLS/155
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/155/">Co
 mputable categoricity relative to a degree</a>\nby Java Darleen Villano (U
 niversity of Connecticut) as part of Online logic seminar\n\n\nAbstract\nA
  computable structure $\\mathcal{A}$ is said to be computably categorical 
 relative to a degree $\\mathbf{d}$ if for all $\\mathbf{d}$-computable cop
 ies $\\mathcal{B}$ of $\\mathcal{A}$\, there exists a $\\mathbf{d}$-comput
 able isomorphism between $\\mathcal{A}$ and $\\mathcal{B}$. In 2021 result
  by Downey\, Harrison-Trainor\, and Melnikov\, it was shown that there exi
 sts a computable graph $\\mathcal{G}$ such that for an infinite increasing
  sequence of c.e.\\ degrees $\\mathbf{x}_0 <_T \\mathbf{y}_0 <_T \\mathbf{
 x}_1 <_T \\mathbf{y}_1\\dots$\, $\\mathcal{G}$ was computably categorical 
 relative to each $\\mathbf{x}_i$ but not computably categorical relative t
 o each $\\mathbf{y}_i$.  That is\, the behavior of categoricity relative 
 to a degree is not monotonic under $\\mathbf{0}'$. In this talk\, we will 
 sketch how to extend this result for partial orders of c.e.\\ degrees\, an
 d discuss some future directions of this project.\n
LOCATION:https://researchseminars.org/talk/OLS/155/
END:VEVENT
END:VCALENDAR