Fully Hilbertian Fields

Details Fully Hilbertian Fields Fully Hilbertian Fields

2009-07-02

arxiv.org/abs/0907.0343v1

Mathematics

Number Theory

Scientific paper

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.

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