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Separably closed fields with higher derivations. I. (English) Zbl 0841.03019
Summary: We define a complete theory \(SHF_e\) of separably closed fields of finite invariant \(e\) (= degree of imperfection) which carry an infinite stack of Hasse-derivations. We show that \(SHF_e\) has quantifier elimination and eliminates imaginaries.

MSC:
03C60 Model-theoretic algebra
12L12 Model theory of fields
03C10 Quantifier elimination, model completeness and related topics
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