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SUMMARY:Theodore Slaman (University of California Berkeley)
DTSTART:20250123T190000Z
DTEND:20250123T200000Z
DTSTAMP:20260423T021309Z
UID:OLS/169
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/169/">Ex
 tending Borel's Conjecture from Measure to Dimension</a>\nby Theodore Slam
 an (University of California Berkeley) as part of Online logic seminar\n\n
 \nAbstract\nWe discuss the general formulation of Hausdorff dimension in t
 erms of gauge measures from the meta-mathematical perspective.  There is a
  natural generalization to the context of dimension of Borel's conjecture 
 that only countable sets have strong measure zero.  We show that this gene
 ralization is consistent with ZFC.  \n\nWe propose the question "For which
  ideals I of gauge measures H does there exist a set such that H(A)>0 exac
 tly when H is an element of I?"  We settle a question of C. Rogers (1962) 
 to show that the answer to this question depends on the descriptive comple
 xity of A.  In particular\, the answer for closed sets is different from t
 hat for (even low-level) Borel sets.\n
LOCATION:https://researchseminars.org/talk/OLS/169/
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