A System of Complete and Consistent Truth
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.
Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1040511340
Mathematical Reviews number (MathSciNet): MR1326116
Digital Object Identifier: doi:10.1305/ndjfl/1040511340
Zentralblatt MATH identifier: 0828.03030