  Łukasiewicz logic can be defined by adding the axiom (known as Wajsberg axiom)\[((\varphi \to \psi) \to \psi) \to ((\psi \to \varphi) \to \varphi)\] to the Hilbert-style proof system for MTL. It corresponds to the finitary version of   the consequence relation defined with respect to evaluations based on the Łukasiewicz t-norm (in symbols: for each finite set of formulas \(\Gamma\) and each formula \(\varphi\), we have \(\Gamma \models_{Ł} \varphi\) iff \(\Gamma \vdash_{Ł}  \varphi\)).[2] 