The undecidability of pseudo real closed fields

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The aim of this note is to establish the following result: THEOREM: Let Ξ be a non-empty class of Boolean spaces and let PRC(Ξ) be the class of pseudo real closed fields whose spaces of orderings belong to Ξ. Then the elementary theory of PRC(Ξ) is undecidable. Our proof appears to be an interesting application of the theory of Artin-Schreier structures, which has been initiated in [5] for the purpose of characterization of the absolute Galois groups of PRC fields. In Section 1 we define and investigate Frattini covers of Artin-Schreier structures, in analogy with [6], Section 2. In Section 2 we consider the analogues of proofs of [1] and [3], to attain the Theorem.

Original languageEnglish
Pages (from-to)91-108
Number of pages18
JournalManuscripta Mathematica
Issue number1
StatePublished - Feb 1984
Externally publishedYes


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