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SUMMARY:Noam Greenberg (Victoria University of Wellington)
DTSTART:20210419T203000Z
DTEND:20210419T213000Z
DTSTAMP:20260423T005725Z
UID:CTA/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/47/">The
  strength of Borel Wadge comparability</a>\nby Noam Greenberg (Victoria Un
 iversity of Wellington) as part of Computability theory and applications\n
 \n\nAbstract\nWadge’s comparability lemma says that the Borel sets are a
 lmost linearly ordered under Wadge reducibility: for any two Borel sets A 
 and B\, either A is a continuous pre-image of B\, or B is a continuous pre
 -image of the complement of A. Wadge’s proof uses Borel determinacy\, wh
 ich is not provable in second order arithmetic (H. Friedman). Using deep a
 nd complex techniques\, Louveau and Saint-Raymond showed that Borel Wadge 
 comparability is provable in second order arithmetic\, but did not explore
  its precise proof-theoretic strength. I will discuss recent work aiming t
 o clarify this.\n\nOne of the main technical tools we use is Montalbán’
 s “true stage” machinery\, originally developed for iterated priority 
 constructions in computable structure theory\, but more recently used by D
 ay and Marks for their resolution of the decomposability conjecture.\n\nJo
 int work with Adam Day\, Matthew Harrison-Trainor\, and Dan Turetsky.\n
LOCATION:https://researchseminars.org/talk/CTA/47/
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