A system of complete and consistent truth

Abstract

To the axioms of Peano arithmetic formulated in a language with an additional unary predicate symbol T we add the rules of necessitation φ T φ and conecessitation T φ and axioms stating that T commutes with the logical connectives and quantifiers. By a result of McGee this theory is ω-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. © 1994, Duke University Press. All Rights Reserved.