Existentially closed fields with holomorphy rings
type: Item
instance of: scholarly article
title: Existentially closed fields with holomorphy rings
zbMATH Open document ID: 0874.03047
author: Joachim Schmid
published in: Archive for Mathematical Logic
publication date: 1997-11-05T00:00:00Z
review text: The paper studies the existence of a model companion for a theory of fields with a predicate for a subring. Precisely it is shown that the theory of fields together with an integrally closed subring, the theory of formally real fields with a real holomorphy ring and the theory of formally \(p\)-adic fields with a \(p\)-adic holomorphy have no model companions in the language of fields augmented by a unary predicate for the corresponding ring. Key facts are that any existentially closed model of each of these theories is not a field and a kind of local-global transfer principle for existentially closed models of these theories.
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 12L12
Mathematics Subject Classification ID: 03C52
zbMATH DE Number: 1006564
zbMATH Keywords: existence of a model companion
zbMATH Keywords: theory of fields with a predicate for a subring
zbMATH Keywords: integrally closed subring
zbMATH Keywords: formally real fields
zbMATH Keywords: real holomorphy ring
zbMATH Keywords: formally \(p\)-adic fields
zbMATH Keywords: \(p\)-adic holomorphy
zbMATH Keywords: existentially closed model
zbMATH Keywords: local-global transfer principle
reviewed by: Christian Michaux
MaRDI profile type: Publication
full work available at URL: s001530050058
OpenAlex ID: W2029767764
DOI: 10.1007/S001530050058
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description: scientific article; zbMATH DE number 1006564