An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Łukasiewicz
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.
scientific article; zbMATH DE number 994532