This work presents a model-theoretic approach to the study of first-order theories of classes of BL-chains. Among other facts, we present several classes of BL-algebras, generating the whole variety of BL-algebras, whose first-order theory has quantifier elimination. Model-completeness and decision problems are also investigated. Then we investigate classes of BL-algebras having (or not having) the amalgamation property or the joint embedding property and we relate the above properties to the existence of ultrahomogeneous models.
"Quantifier Elimination and Other Model-Theoretic Properties of BL-Algebras." Notre Dame J. Formal Logic 52 (4) 339 - 379, 2011. https://doi.org/10.1215/00294527-1499336