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RRC-fields with small absolute Galois groups. (English) Zbl 0691.12012
Let \(RRC_ n\) be the class of all regular real closed fields (RRC- fields) of zero characteristic with Galois group G(F) having a system of generators \(\sigma_ 1,\sigma_ 2,...,\sigma_ n\) such that any linear order L on F is the restriction of the unique order on \(\tilde F^{\sigma}\) for some involution \(\sigma \in \{\sigma_ 1,\sigma_ 2,...,\sigma_ n\}.\)
The main result is: The elementary theory \(Th(RRC_ n)\) of the class \(RRC_ n\) is decidable for any \(n\in \omega\).
Reviewer: D.Busneag

MSC:
12L05 Decidability and field theory
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