“Arithmetic and Truth in Łukasiewicz’s Infinitely Valued Logic,” Logique et Analyse, 36 (1993) 25–38 (published in 1995).
Peano arithmetic formulated in Łukasiewicz’s infinitely valued logic collapses into classical Peano arithmetic. However, not all additions to the language need also be classical. The way is open for the addition of a real truth predicate satisfying the T-scheme into the language. However, such an addition is not pleasing. The resulting theory is omega-inconsistent. This paper consists of the proofs and interpretations of these two results.