Bases of admissible rules of proper axiomatic extensions of Łukasiewicz logic

In this paper we give a base of admissible rules for every proper axiomatic extension of the infinite valued Łukasiewicz logic. We first prove that single-conclusion admissible rules of any proper axiomatic extension are finitely based. The proof strongly relies on the characterization of least V-quasivarieties given in [11].