Abstract
We introduce MV-algebras by means of a small number of simple equations, in an attempt to capture certain properties of the unit real interval [0,1] equipped with truncated addition x ⊕ y = min(1, x + y) and negation 1 - x. We show that every MV-algebra contains a natural lattice-order. The chapter culminates with Chang’s Subdirect Representation Theorem, stating that if an equation holds in all totally ordered MV-algebras, then the equation holds in all MV-algebras.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Cignoli, R.L.O., D’Ottaviano, I.M.L., Mundici, D. (2000). Basic notions. In: Algebraic Foundations of Many-Valued Reasoning. Trends in Logic, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9480-6_2
Download citation
DOI: https://doi.org/10.1007/978-94-015-9480-6_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5336-7
Online ISBN: 978-94-015-9480-6
eBook Packages: Springer Book Archive