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SUMMARY:Paul Shafer (University of Leeds)
DTSTART:20201110T210000Z
DTEND:20201110T220000Z
DTSTAMP:20260423T005719Z
UID:CTA/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/27/">Ran
 domness notions and reverse mathematics</a>\nby Paul Shafer (University of
  Leeds) as part of Computability theory and applications\n\n\nAbstract\nTh
 ere are many notions of algorithmic randomness in addition to classic Mart
 in-Löf randomness\, such as 2-randomness\, weak 2-randomness\, computable
  randomness\, and Schnorr randomness.  For each notion of randomness\, we 
 consider the statement "For every set Z\, there is a set X that is random 
 relative to Z" as a set-existence principle in second-order arithmetic\, a
 nd we compare the strengths of these principles.  We also show that a well
 -known characterization of 2-randomness in terms of incompressibility can 
 be proved in RCA_0\, which is non-trivial because it requires avoiding the
  use of $\\Sigma^0_2$ bounding.\n
LOCATION:https://researchseminars.org/talk/CTA/27/
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