TY - JOUR
T1 - On algebraically closed fields with a distinguished subfield
AU - d’Elbée, Christian
AU - Kaplan, Itay
AU - Neuhauser, Leor
N1 - Publisher Copyright:
© The Hebrew University of Jerusalem 2024.
PY - 2024/10
Y1 - 2024/10
N2 - This paper is concerned with the model-theoretic study of pairs (K, F) where K is an algebraically closed field and F is a distinguished subfield of K allowing extra structure. We study the basic model-theoretic properties of those pairs, such as quantifier elimination, model-completeness and saturated models. We also prove some preservation results of classification-theoretic notions such as stability, simplicity, NSOP1, and NIP. As an application, we conclude that a PAC field is NSOP1 iff its absolute Galois group is (as a profinite group).
AB - This paper is concerned with the model-theoretic study of pairs (K, F) where K is an algebraically closed field and F is a distinguished subfield of K allowing extra structure. We study the basic model-theoretic properties of those pairs, such as quantifier elimination, model-completeness and saturated models. We also prove some preservation results of classification-theoretic notions such as stability, simplicity, NSOP1, and NIP. As an application, we conclude that a PAC field is NSOP1 iff its absolute Galois group is (as a profinite group).
UR - https://www.scopus.com/pages/publications/85191710206
U2 - 10.1007/s11856-024-2621-1
DO - 10.1007/s11856-024-2621-1
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AN - SCOPUS:85191710206
SN - 0021-2172
VL - 263
SP - 169
EP - 211
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -