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SUMMARY:Which Weihrauch degrees correspond to axiom systems? - Vasco Bratt
 ka (Universität der Bundeswehr München\, University of Cape Town)
DTSTART:20220610T090000Z
DTEND:20220610T100000Z
UID:TALK174842@talks.cam.ac.uk
DESCRIPTION:Weihrauch complexity can be seen as a more uniform version of 
 different varieties of reverse mathematics. This is true\, in particular\,
  for classical reverse mathematics (in the sense of Friedman and Simpson) 
 as well as for constructive reverse mathematics (in the sense of Ishihara)
  and probably for other varieties too. In both cases "more uniform" only h
 olds modulo certain additional differences. In both cases the question app
 ears\, when certain Weihrauch degrees legitimately correspond to certain a
 xiom systems. In some cases\, such as WKL\, there is a widely accepted ans
 wer to this question. In other cases\, such as ATR or induction and bounde
 dness principles\, this is debated somewhat controversially. We will propo
 se a thesis that can be used as a necessary condition for legitimacy and i
 t roughly says that the theories of the respective axiom systems should co
 rrespond to the lower cones of the corresponding Weihrauch degrees. This l
 eads to a discussion of closure under compositional product and paralleliz
 ation.
LOCATION:Seminar Room 1\, Newton Institute
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