TY - JOUR
T1 - Fully Hilbertian fields
AU - Bary-Soroker, Lior
AU - Paran, Elad
PY - 2013/3
Y1 - 2013/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84876926668&partnerID=8YFLogxK
U2 - 10.1007/s11856-012-0153-6
DO - 10.1007/s11856-012-0153-6
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AN - SCOPUS:84876926668
SN - 0021-2172
VL - 194
SP - 507
EP - 538
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -