Fully Hilbertian fields

Lior Bary-Soroker, Elad Paran

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)507-538
Number of pages32
JournalIsrael Journal of Mathematics
Issue number2
StatePublished - Mar 2013
Externally publishedYes


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