RETRACTED ARTICLE: A Completeness Theorem for a Functionally Complete Łukasiewicz Logic: This article was retracted on April 9, 2026 - Aranda, Víctor (Logic and Logical Philosophy, 2025)
This article was retracted on April 9, 2026 The Editors-in-Chief have retracted this article because, after publication, it became apparent that it cites Mateusz Radzki's paper (2017), which contains an error in the proof of the claim that Słupecki's three-valued system is incomplete. Therefore, based on Radzki's paper, it cannot be concluded that Słupecki's system is really incomplete. Although the results contained in Víctor Aranda's LLP paper are not formally dependent on the content of Radzki's text, we have decided to ask the author to withdraw the original submission and prepare its corrected version. The corrected version is available at https://doi.org/10.12775/LLP.2026.010. We want to express our profound gratitude to Professor Jan Zygmunt for his consultations and for pointing out the reference to Radzki's erroneous proof of claim that Słupecki's system is incomplete. Supplementary Information Below is the link to the electronic supplementary material: Supplementary file (download PDF)