Title On Lukasiewicz logic with truth constants Publication Type Book Chapter Year of Publication 2007 Authors Cignoli R, Esteva F, Godo L Editor O. al. Cet Book Title Theoretical Advances and Applications of Fuzzy Logic and Soft Computing, ASC 42 Pagination 869-875 Publisher Springer-Verlag Abstract Canonical completeness results for {Ł}$(\mathcal{C})$, the expansion of {Ł}ukasiewicz logic {Ł} 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 {Ł}$(\mathcal{C})$ is strongly canonical complete for finite theories for {\em any} countable subalgebra $\mathcal{C}$ of the standard {Ł}ukasiewicz chain $[0,1]_{Ł}$.