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Fully Hilbertian fields

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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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Authors and Affiliations

  1. Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram The Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Lior Bary-Soroker

  2. School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Elad Paran

Authors
  1. Lior Bary-Soroker
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  2. Elad Paran
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Correspondence to Lior Bary-Soroker.

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Bary-Soroker, L., Paran, E. Fully Hilbertian fields. Isr. J. Math. 194, 507–538 (2013). https://doi.org/10.1007/s11856-012-0153-6

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  • DOI: https://doi.org/10.1007/s11856-012-0153-6

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