An approach to Julia Robinson numbers through the lattice of subfields

Abstract

By fully describing the lattice of subfields of some towers of number fields built by iterating square roots, we obtain infinitely many fields, each of them either contradicts Julia Robinson's problem (obtaining a JR-number $4$ which is not a minimum) or gives a Julia Robinson number strictly between four and infinity. This improves a previous result by M. Castillo and the same authors.