The \({\mathcal L}^{<\omega}\)-theory of the class of Archimedian real closed fields
type: Item
instance of: scholarly article
title: The \({\mathcal L}^{<\omega}\)-theory of the class of Archimedian real closed fields
zbMATH Open document ID: 0682.03018
DOI: 10.1007/BF01622875
author: Gerd Bürger
published in: Archive for Mathematical Logic
publication date: 1989-01-01T00:00:00Z
review text: For the class \({\mathcal A}\) of Archimedian real closed fields it is shown that the Malitz quantifier \(Q^ n\) is eliminable over \({\mathcal A}\), provably in ZFC, if \(n\leq 2\). If the Continuum-Hypothesis (CH) is true, \(Q^ 3\), hence any \(Q^ n\) for \(n\geq 3\), cannot be eliminated over \({\mathcal A}\). Conversely, it is consistent with ZFC that every \(Q^ n\), for \(n\geq 1\), is eliminable over \({\mathcal A}\); the last statement is already a consequence of the Proper-Forcing-Axiom.
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 12L12
Mathematics Subject Classification ID: 03C10
Mathematics Subject Classification ID: 03C80
Mathematics Subject Classification ID: 03E50
zbMATH DE Number: 4116508
zbMATH Keywords: Malitz logic
zbMATH Keywords: Archimedian real closed fields
zbMATH Keywords: Malitz quantifier
zbMATH Keywords: Continuum-Hypothesis
zbMATH Keywords: Proper-Forcing-Axiom
MaRDI profile type: Publication
cites work: Q3220578
cites work: Q3037421
cites work: Q3916558
cites work: Set theory. An introduction to independence proofs
cites work: The ordered field of real numbers and logics with Malitz quantifiers
cites work: Proper forcing
full work available at URL: https://doi.org/10.1007/bf01622875
OpenAlex ID: W2024769114
description: scientific article; zbMATH DE number 4116508