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SUMMARY:Andrew Marks (UCLA)
DTSTART:20200728T210000Z
DTEND:20200728T220000Z
DTSTAMP:20260423T005653Z
UID:CTA/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/15/">Pri
 ority arguments in descriptive set theory</a>\nby Andrew Marks (UCLA) as p
 art of Computability theory and applications\n\n\nAbstract\nWe give a new 
 characterization of when a Borel set is\nSigma^0_n complete for n at at le
 ast 3. This characterization is\nproved using Antonio Montalb\\'an's true 
 stages machinery for\nconducting priority arguments.\n\nAs an application\
 , we prove the decomposability conjecture in\ndescriptive set theory assum
 ing projective determinacy. This\nconjecture characterizes precisely which
  Borel functions are\ndecomposable into a countable union of continuous fu
 nctions with\n$\\Pi^0_n$ domains. Our proof also uses a theorem of Leo Har
 rington\nthat assuming the axiom of determinacy there is no $\\omega_1$ le
 ngth\nsequence of distinct Borel sets of bounded rank. This is joint work\
 nwith Adam Day.\n
LOCATION:https://researchseminars.org/talk/CTA/15/
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