Structurally complete finitary extensions of positive Łukasiewicz logic

Abstract In this paper we study $\mathcal{M}\mathcal{V}^{+}$, i.e. the positive fragment of Łukasiewicz infinite-valued Logic $\mathcal{M}\mathcal{V}$. Using mainly algebraic techniques we characterize all the finitary extensions of $\mathcal{M}\mathcal{V}^{+}$ that are structurally complete and those that are hereditarily structurally complete.