RRC-fields with small absolute Galois groups
type: Item
instance of: scholarly article
title: RRC-fields with small absolute Galois groups
zbMATH Open document ID: 0691.12012
DOI: 10.1016/0168-0072(89)90068-7
published in: Annals of Pure and Applied Logic
publication date: 1989-01-01T00:00:00Z
review text: 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 \(n\in \omega\).
reviewed by: Dimitru Buşneag
Mathematics Subject Classification ID: 12L05
zbMATH DE Number: 4130501
zbMATH Keywords: decidability
zbMATH Keywords: regular real closed fields
zbMATH Keywords: RRC-fields
zbMATH Keywords: elementary theory
author: Yuri L. Ershov
MaRDI profile type: Publication
full work available at URL: 0168-0072(89)90068-7
OpenAlex ID: W2083099903
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description: scientific article; zbMATH DE number 4130501