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SUMMARY:Steve Jackson (University of North Texas)
DTSTART:20210914T123000Z
DTEND:20210914T133000Z
DTSTAMP:20260423T052836Z
UID:OWNS/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/55/">De
 scriptive complexity in numeration systems</a>\nby Steve Jackson (Universi
 ty of North Texas) as part of One World Numeration seminar\n\n\nAbstract\n
 Descriptive set theory gives a means of calibrating the complexity of sets
 \, and we focus on some sets occurring in numerations systems. Also\, the 
 descriptive complexity of the difference of two sets gives a notion of the
  logical independence of the sets. A classic result of Ki and Linton says 
 that the set of normal numbers for a given base is a $\\boldsymbol{\\Pi}^0
 _3$ complete set. In work with Airey\, Kwietniak\, and Mance we extend to 
 other numerations systems such as continued fractions\, $\\beta$-expansion
 s\, and GLS expansions. In work with Mance and Vandehey we show that the n
 umbers which are continued fraction normal but not base $b$ normal is comp
 lete at the expected level of $D_2(\\boldsymbol{\\Pi}^0_3)$. An immediate 
 corollary is that this set is uncountable\, a result (due to Vandehey) onl
 y known previously assuming the generalized Riemann hypothesis.\n
LOCATION:https://researchseminars.org/talk/OWNS/55/
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