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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20240313T143000
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DTEND;TZID=America/Toronto:20240313T153000
URL:https://uwaterloo.ca/pure-mathematics/events/logic-seminar-61
SUMMARY:Logic Seminar
CLASS:PUBLIC
DESCRIPTION:JOEY LAKERDAS-GAYLE\, DEPARTMENT OF PURE MATHEMATICS\, UNIVERSI
 TY OF\nWATERLOO\n\n\"ISOMORPHISM SPECTRA AND COMPUTABLY COMPOSITE STRUCTUR
 ES\"\n\nIf $\\mathcal{A}$ and $\\mathcal{B}$ are two computable copies of 
 a\nstructure\, their isomorphism spectrum is the set of Turing degrees\nth
 at compute an isomorphism from $\\mathcal{A}$ to $\\mathcal{B}$. We\nintro
 duce a framework for constructing computable structures with the\nproperty
  that the isomorphisms between arbitrary computable copies of\nthese struc
 tures are constructed from isomorphisms between computable\ncopies of thei
 r component structures. We call these \\emph{computably\ncomposite structu
 res}. We show that given any uniformly computable\ncollection of isomorphi
 sm spectra\, there exists a pair of computably\ncomposite structures whose
  isomorphism spectrum is the union of the\noriginal isomorphism spectra. W
 e use this to construct examples of\nisomorphism spectra that are not equa
 l to the upward closure of any\nfinite set of Turing degrees.\n\nMC 5479
DTSTAMP:20260506T035148Z
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