arXiv subjects
Publications and source records attributed to Carlos R. Videla.
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.
It is shown that the compositum $ \mathbb Q^{(2)}$ of all degree 2 extensions of $\mathbb Q$ has undecidable theory.
We compare three different characterizations, due respectively to R. Dedekind, K. Uchida, and H. Lüneburg, of when $\mathbb Z[θ]$ is the ring of integers of $\mathbb Q(θ)$, and apply our results to some concrete $2$-towers of number fields.
For rings $\mathcal{O}_K$ of totally real algebraic integers, J. Robinson defined a set which is always $\{+\infty\}$ or of the form $[λ,+\infty)$ or $(λ,+\infty)$ for some real number $λ\ge4$. All known examples give either $\{+\infty\}$ or $[4,+\infty)$. In this paper, we construct infinitely many fields such that the set is an interval, but not equal to $[4,+\infty)$.