An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Łukasiewicz
type: Item
instance of: scholarly article
title: An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Łukasiewicz
zbMATH Open document ID: 0876.03011
DOI: 10.1023/A:1004991931741
author: Daniele Mundici
author: Roberto Cignoli
published in: Studia Logica
publication date: 1997-10-30T00:00:00Z
review text: This paper presents a self-contained proof of Chang's completeness theorem for Łukasiewicz's infinite valued calculus. Some basic properties of MV-algebras are introduced. It is shown that the unit interval \([0,1]\) with the operations \(\neg x = 1-x \) and \( x \oplus y = \min(1,x+y) \) is an initial MV-algebra, in the sense that an equation holds in \([0,1]\) if and only if it holds in every MV-algebra. This yields Chang{'}s completeness theorem.
reviewed by: Albert Hoogewijs
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 06D30
zbMATH DE Number: 994532
zbMATH Keywords: many-valued logic
zbMATH Keywords: Łukasiewicz calculus
zbMATH Keywords: MV algebra
zbMATH Keywords: Chang's completeness theorem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 994532