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SUMMARY:Xavier Vidaux (Universidad de Concepción)
DTSTART:20220825T180000Z
DTEND:20220825T190000Z
DTSTAMP:20260423T021340Z
UID:OLS/97
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/97/">Tow
 ers of totally real nested square roots: undecidability\, the lattice of s
 ubfields\, and the quartic extensions within the tower</a>\nby Xavier Vida
 ux (Universidad de Concepción) as part of Online logic seminar\n\n\nAbstr
 act\nAfter recalling some first order undecidability results in infinite a
 lgebraic extensions of the field of rational numbers\, I will talk about a
  concrete family of 2-towers of totally real number fields\, namely\, $(\\
 mathbb{Q}(x_n))_{n\\ge0}$\, where $x_{n+1}=\\sqrt{\\nu+x_n}$ for some give
 n positive integers $\\nu$ and $x_0$. Let $K$ be the union of the $\\mathb
 b{Q}(x_n)$. Though these fields $K$ are somewhat the simplest subfields of
  an algebraic closure of $\\mathbb{Q}$ that one may construct\, they hide 
 a rich variety of natural problems of topological\, algebraic\, dynamical 
 and logical nature. The results that I will present about these fields are
  due to M. Castillo\, C. Videla\, and who writes.\n
LOCATION:https://researchseminars.org/talk/OLS/97/
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