Fully Hilbertian Fields
Number Theory
2009-07-03 v1 Commutative Algebra
Abstract
We introduce the notion of fully Hilbertian fields, a strictly stronger notion than that of Hilbertian fields. We show that this class of fields exhibits the same good behavior as Hilbertian fields, but for fields of uncountable cardinality, is more natural than the notion of Hilbertian fields. In particular, we show it can be used to achieve stronger Galois theoretic results. Our proofs also provide a step toward the so-called Jarden-Lubotzky twinning principle.
Keywords
Cite
@article{arxiv.0907.0343,
title = {Fully Hilbertian Fields},
author = {Lior Bary-Soroker and Elad Paran},
journal= {arXiv preprint arXiv:0907.0343},
year = {2009}
}