@inbook {IIIA-2007-1533,
title = {On Lukasiewicz logic with truth constants},
booktitle = {Theoretical Advances and Applications of Fuzzy Logic and Soft Computing, ASC 42},
year = {2007},
pages = {869-875},
publisher = {Springer-Verlag},
organization = {Springer-Verlag},
abstract = {Canonical completeness results for {{\L}}$(\mathcal{C})$, the expansion of {{\L}}ukasiewicz logic {{\L}} with a countable set of truth-constants $\mathcal{C}$, have been recently proved in \cite{eggn06} for the case when the algebra of truth constants $\mathcal{C}$ is a subalgebra of the rational interval $[0, 1] \cap \mathbb{Q}$. The case when $C \not \subseteq [0, 1] \cap \mathbb{Q}$ was left as an open problem. In this paper we solve positively this open problem by showing that {{\L}}$(\mathcal{C})$ is strongly canonical complete for finite theories for {\em any} countable subalgebra $\mathcal{C}$ of the standard {{\L}}ukasiewicz chain $[0,1]_{{\L}}$.},
author = {Roberto Cignoli and Francesc Esteva and Llu{\'\i}s Godo},
editor = {O. Castillo et al.}
}