Technical Report TR-ARP-6-94

Automated Reasoning Project
Research School of Information Sciences and Engineering
and Centre for Information Science Research
Australian National University

March 30, 1994

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 !-inconsistent. This paper consists of the proofs and interpretations of these two results.