The field of reals with a predicate for the powers of two
type: Item
instance of: scholarly article
title: The field of reals with a predicate for the powers of two
zbMATH Open document ID: 0631.03020
DOI: 10.1007/BF01171706
published in: Manuscripta Mathematica
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155108
review text: Let L be the language of ordered rings augmented by a 1-place relation symbol. Consider the ordered field \({\mathbb{R}}\) of reals together with the multiplicative group \(2^{{\mathbb{Z}}}=\{2^ n:n\in {\mathbb{Z}}\}\) as an L- structure. The author provides a set \(\Sigma\) of axioms for the complete, decidable L-theory \(Th({\mathbb{R}},2^{{\mathbb{Z}}})\). Augmenting L by countably many 1-place relation symbols and \(\Sigma\) by defining axioms for the new symbols, one gets a theory which admits elimination of quantifiers.
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 12L12
Mathematics Subject Classification ID: 12J15
Mathematics Subject Classification ID: 03C10
Mathematics Subject Classification ID: 03C65
zbMATH DE Number: 4025415
zbMATH Keywords: complete theory
zbMATH Keywords: archimedean class
zbMATH Keywords: saturated elementary extension
author: Lou van den Dries
reviewed by: Şerban A. Basarab
MaRDI profile type: Publication
cites work: Algebraic theories with definable Skolem functions
cites work: Lectures on formally real fields
cites work: Q5652669
OpenAlex ID: W1967705670
description: scientific article; zbMATH DE number 4025415