Fully Hilbertian fields

Lior Bary-Soroker; Elad Paran

doi:10.1007/s11856-012-0153-6

Fully Hilbertian fields

Lior Bary-Soroker
, Elad Paran

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	507-538
Number of pages	32
Journal	Israel Journal of Mathematics
Volume	194
Issue number	2
DOIs	https://doi.org/10.1007/s11856-012-0153-6
State	Published - Mar 2013
Externally published	Yes

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10.1007/s11856-012-0153-6

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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.",

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Fully Hilbertian fields

Abstract

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