Arithmetic and truth in Lukasiewicz's infinitely valued logic

Greg Restall

Abstract


Peano arithmetic formulated in Lukasiewicz'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.

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