Towers of totally real nested square roots: undecidability, the lattice of subfields, and the quartic extensions within the tower

Xavier Vidaux (Universidad de Concepción)

25-Aug-2022, 18:00-19:00 (3 years ago)

Abstract: After recalling some first order undecidability results in infinite algebraic extensions of the field of rational numbers, I will talk about a concrete family of 2-towers of totally real number fields, namely, (Q(xn))n0(\mathbb{Q}(x_n))_{n\ge0}, where xn+1=ν+xnx_{n+1}=\sqrt{\nu+x_n} for some given positive integers ν\nu and x0x_0. Let KK be the union of the Q(xn)\mathbb{Q}(x_n). Though these fields KK are somewhat the simplest subfields of an algebraic closure of Q\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.

commutative algebralogicnumber theory

Audience: researchers in the topic


Online logic seminar

Series comments: Description: Seminar on all areas of logic

Organizer: Wesley Calvert*
*contact for this listing

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