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SUMMARY:Andre Nies (Auckland University)
DTSTART:20210503T203000Z
DTEND:20210503T213000Z
DTSTAMP:20260423T024530Z
UID:CTA/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/48/">Max
 imal towers and ultrafilter bases in computability theory</a>\nby Andre Ni
 es (Auckland University) as part of Computability theory and applications\
 n\n\nAbstract\nThe tower number and ultrafilter numbers are cardinal chara
 cteristics from set theory that are defined in terms of sets of natural nu
 mbers with almost inclusion. The former is the least size of a maximal tow
 er. The latter is the least size of a collection of infinite sets with upw
 ard closure a non-principal ultrafilter. \n\nTheir analogs in computabilit
 y theory will be defined in terms of collections of computable sets\, give
 n as the columns of a single set. We study their complexity using Medvedev
  reducibility. For instance\, we show that the ultrafilter number is Medve
 dev equivalent to the problem of finding a function that dominates all com
 putable functions\, that is\, highness. In contrast\, each nonlow set unif
 ormly computes a maximal tower. \n\nJoint work with Steffen Lempp\, Joseph
  Miller\, and Mariya Soskova\n
LOCATION:https://researchseminars.org/talk/CTA/48/
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