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Groups and fields interpretable in separably closed fields. (English) Zbl 0803.03023
Summary: We prove that any infinite group interpretable in a separably closed field \(F\) of finite Ershov-invariant is definably isomorphic to an \(F\)- algebraic group. Using this result we show that any infinite field \(K\) interpretable in a separably closed field \(F\) is itself separably closed; in particular, in the finite invariant case \(K\) is definably isomorphic to a finite extension of \(F\).

MSC:
03C60 Model-theoretic algebra
12L12 Model theory of fields
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