Comparing several calculi for first-order infinite-valued Łukasiewicz logic

Abstract: From the viewpoint of provability, we compare some Gentzen-type hypersequent calculi for first-order infinite-valued {\L}ukasiewicz logic and for first-order rational Pavelka logic with each other and with H\'ajek's Hilbert-type calculi for these logics. The key aspect of our comparison is a density elimination proof for one of the hypersequent calculi considered.