A System of Complete and Consistent Truth

Notre Dame Journal of Formal Logic 35 (1):311--27 (1994)
Abstract
To the axioms of Peano arithmetic formulated in a language with an additional unary predicate symbol T we add the rules of necessitation and conecessitation T and axioms stating that T commutes with the logical connectives and quantifiers. By a result of McGee this theory is -inconsistent, but it can be approximated by models obtained by a kind of rule-of-revision semantics. Furthermore we prove that FS is equivalent to a system already studied by Friedman and Sheard and give an analysis of its proof theory
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Kentaro Fujimoto (2012). Classes and Truths in Set Theory. Annals of Pure and Applied Logic 163 (11):1484-1523.

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