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SUMMARY:Alexandra Shlapentokh (East Carolina University)
DTSTART:20211028T180000Z
DTEND:20211028T190000Z
DTSTAMP:20260423T035744Z
UID:OLS/69
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/69/">A M
 ysterious Ring</a>\nby Alexandra Shlapentokh (East Carolina University) as
  part of Online logic seminar\n\n\nAbstract\nLet ${\\mathbb Q}^{\\text{ab}
 }$ be the largest abelian extension of $\\mathbb Q$\, or in other words th
 e compositum of all cyclotomic extensions.  Let $O_{{\\mathbb Q}^{\\text{a
 b}}}$ be the ring of integers of ${\\mathbb Q}^{\\text{ab}}$ or the ring o
 f elements of ${\\mathbb Q}^{\\text{ab}}$ satisfying monic irreducible pol
 ynomials over $\\mathbb Z$.  It is not known whether the first-order theor
 y of $O_{{\\mathbb Q}^{\\text{ab}}}$ is decidable.  ${\\mathbb Q}^{\\text{
 ab}}$ is also a degree two extension of a totally real field.  Much more i
 s known about the first-order theory of rings of integers of totally real 
 fields and in some cases one is able to deduce undecidability of the first
 -order theory of the ring of integers of a degree 2  extension of a totall
 y real field from an analogous result for the ring of integers of the tota
 lly real field.  However this method does not seem to work for ${\\mathbb 
 Q}^{\\text{ab}}$.  We discuss a possible way of resolving this problem and
  some related questions.\n
LOCATION:https://researchseminars.org/talk/OLS/69/
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