Up to categorical equivalence, abelian lattice-ordered groups with strong unit coincide with Chang's MV-algebrasᎏthe Lindenbaum algebras of the infinite-valued Łukasiewicz calculus. While the property of being a strong unit is not definable even in first-order logic, MV-algebras form an equational c
Universal Classes of MV-chains with Applications to Many-valued Logics
✍ Scribed by Joan Gispert
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 304 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
In this paper we characterize, classify and axiomatize all universal classes of MV-chains. Moreover, we accomplish analogous characterization, classification and axiomatization for congruence distributive quasivarieties of MV-algebras. Finally, we apply those results to study some finitary extensions of the Lukasiewicz infinite valued propositional calculus.
📜 SIMILAR VOLUMES
## Abstract It is known (see Rapp [9]) that elementary geometry with the additional quantifier “there exist uncountably many” is decidable. We show that this decidability helps in solving the following problem from combinatorial geometry: does there exist an uncountable family of pairwise non‐congr